Verifying Inverse Functions In Exercises 13-16, verify that f and g are inverse functions. f(x) = -7/2x - 3, g(x) = - 2x + 6/7 Solution given f(x)=-(7/2)x -3 ,g(x)=-(2x+6)/7 (fog)(x) =f(g(x)) =f(-(2x+6)/7) =-(7/2)(-(2x+6)/7) -3 =((2x+6)/2) -3 =x+3 -3 =x (gof)(x) =g(f(x)) =g(-(7/2)x -3) =-(2(-(7/2)x -3) +6)/7 =-((-7x -6) +6)/7 =-(-7x)/7 =7x/7 =x (fog)(x)=(fog)(x) =x so f and g are inverse functions.

1. what is the appropriate awareness level and safety knowledge required for the modification of a
safety program?
Solution
Answer :
Mounting evidence suggests that incorporating the principles of corporate social responsibility
and sustainable development into organizational decision-making processes has fundamentally
changed the way business is being conducted. Driven in large part by consumer and investor
demand, organizations’ business strategies now commonly consider the impact of corporate
activities on the environment, consumers, employees, communities, and other stakeholders.
This has led to new approaches to problem solving, redefined corporate priorities, reallocated
budgets, and redesigned staffing responsibilities. These changes have significant ramifications
for safety management. Occupational safety and health is generally categorized as part of an
organization’s commitment to social responsibility. Several key safety indicators are included as
part of the leading global sustainability indices. Safety professionals must drive safety
sustainability efforts by ensuring that their organizations recognize that the safety, health, and
well-being of workers, customers, and neighboring communities are among the primary
considerations in any business practices, operations or development. Safety professionals also
need a good working knowledge of environmental issues related to sustainability, key
sustainability metrics, and the key drivers of sustainability.
The candidate should discuss how he or she analyzed the information to look for trends,
breakdowns in processes, or other deficiencies in the safety program. He or she should be able to
give examples of instances where the candidate’s analysis led to modifications of the safety
program (new training, additional inspections, increased involvement by managers, etc.).The
candidate should also discuss how he or she communicated the findings to management or
employees. (E.g., “I used the information as a way to interact with employees to keep safety in
the front of their minds.” “I would celebrate our successes with them and ask for their input on
ways to improve our performance.”)
Several issues come into play here. The first is that you want to ensure that the noncompliant
behavior is corrected immediately so that the employee is not at risk. Secondly, you should
verify that other employees are following required safe work practices, even beyond the issue of
the head protection. Finally, you want to be sensitive to the fact that the employee who informed

2. you of the non-compliant behavior may be ostracized by his or her coworkers if the details of the
report were made public. One approach is to have group or department
meetings to reiterate rules and enforcement policies (including a discussion of the wearing of
head protection), increase awareness, identify gaps in training, and to remind employees of their
safety-related responsibilities.
IMPLEMENTATION OF A SAFETY PROGRAMME
Tom B. Leamon
The implementation of a safety programme should reflect its nature as a normal, day-to-day
concern of general management. The need for information for decision making at all stages and
for communication between all levels of the enterprise form the basis for successful
implementation of such a programme.
Executive Level
Initially, the introduction of a new or modified safety programme will require the agreement of
senior management, who may regard it as a cost/benefit decision to be made in light of
competition for resources from elsewhere in the enterprise. The desire to reduce damages, pain
and suffering in the workplace through the implementation of a safety programme will be
tempered by the organization’s ability to sustain such an effort. Informed management decisions
will require three elements:
1. an explicit description of the programme, which fully defines the proposed approach
2. an assessment of the impact of the programme on the company operations
3. an estimate of the costs of implementation with a prediction of the benefits that are likely to
be produced.
The only exception to this will be when a safety programme is mandated by regulation and must
be instituted in order to remain in business.
In the latter endeavour, it is useful to add an estimate of the true costs of the current safety record
of the enterprise, as well as those costs covered by direct insurance or direct out-of-pocket
expenses. The indirect costs are likely to be significant in all cases; estimates for serious
incidents in the United Kingdom suggest that the real costs (borne by an enterprise as indirect
costs) range from a factor of two to three up to a factor of ten times the actual, direct insurance
costs. In those countries requiring compulsory insurance, the cost, and hence the savings, will
vary widely depending on the social environment of each particular nation. Insurance costs in
countries where the insurance carriers are required to cover full medical and rehabilitation costs,
such as the United States, are likely to be higher than those in countries in which the treatment of
the injured worker is part of the social contract. An ideal way to emphasize the significance of
such losses is to identify the annual production required to generate revenue lost in paying for
these losses. This is highly compatible with the concept that, while a business must necessarily

3. assume the risk of doing business, it should be managing that risk in order to reduce the losses
and improve its financial performance.
Management Level
Following acceptance at the senior management level, an implementation team should be formed
to develop the strategy and the plan to introduce the programme of the roll-out plan. Such an
approach is more likely to be effective than one that shifts the responsibility for safety to an
individual designated as the safety engineer. The size and level of the involvement of this
implementation team will vary widely, depending on the enterprise and the social environment.
Nevertheless, input is essential from at least those with responsibility for operations, personnel,
risk management and training, as well as key representatives of employee groups who will be
affected by the programme. It is likely that a team of this composition will detect possible
conflicts (for example, between production and safety) early on in the process, before attitudes
and positions, as well as procedures, hardware and equipment, have become fixed. It is at this
point that collaboration, rather than confrontation, is likely to provide a better opportunity for
problem solving. The output of this team should be a document that identifies the corporate view
of the programme, the key elements of the programme, the schedule for implementation and the
responsibilities of those involved.
Care should be taken to ensure that the executive commitment is particularly evident to managers
at the operational level at which the safety programme can be effected. Perhaps the most
significant way of achieving this is to establish a form of chargeback, or allocation of the true
costs of an accident directly to this level of management. The assumption of medical and
indemnity costs (or their associated insurance costs) as a corporate overhead should be avoided
by management. The unit manager, concerned with day-to-day financial control of the
organization, should have the real costs of inadequate safety programmes appearing on the same
balance sheet as the production and development costs. For example, a unit manager of an
organization in which all the workers’ compensation costs are carried as a corporate overhead
will be unable to justify expenditure of resources to remove a very serious hazard affecting a low
number of workers. This difficulty can occur at the local level, despite the fact that such
expenditures could produce major savings at the corporate level. It is essential that managers
who are responsible for workplace design and operations bear the brunt, or reap the benefits, of
the safety programme for which they are responsible.
Supervisor Level
The supervisor is responsible for understanding, transmitting and ensuring compliance with the
managerial objectives of the safety programme. Successful safety programmes will address the
question of educating and training supervisors in this responsibility. Although special safety
trainers are sometimes used in educating workers, the supervisor should be responsible both for

4. this training and for the attitudes of workers. In particular, informed supervisors see their
responsibility as including the prevention of unsafe acts and exhibiting a high level of intolerance
of unsafe conditions in the workplace. The control of the manufacturing process is accepted as
the mainstream responsibility for supervisors; the application of such control will also produce
benefits in the reduction of damages and unintentional injuries. Regardless of whether the safety
function is staffed by safety officers, joint worker-management committees or consultants, the
day-to-day responsibility for safe, error-free operation of the process should be a written
component in the job description of supervisors.
Worker Level
At the beginning of the century, the primary emphasis for workers to perform safely was placed
on negative reinforcement. Rules were set, workers were expected to follow those rules without
question, and a transgression from the rules subjected the worker to disciplinary action. With
increasingly complicated workplaces, flexible management systems and the rising social
expectations of the workforce, the inadequacies and liabilities of such an approach have been
revealed. It is not only in the military arena that flexibility and responsibility at the local level
appears to be a vital component of high-performance units. This approach has led to an
increasing reliance upon positive reinforcement and empowerment of the workforce, with the
concomitant requirements for education and understanding. This thrust in safety mirrors the
worldwide trend of labour to seek improvements in the quality of working life and the
development of self-directed working groups.
Roll-out Plan
The key elements of the safety programme will identify the requirements for familiarization with
the conceptual basis of the programme, the development of specific safety skills and the
implementation of measurement tools. Responsibilities will be assigned to specific people within
a phased programme at the point of introduction. The end of the roll-out process will be the
establishment of a measurement system, or safety programme audit, in order to assess the
continuing performance of the programme. Appropriate communication must be explicitly
specified in the plan. In many cultures, multiple dialects and languages coexist in the workplace;
and in certain cultures, a “managerial” dialect or language may normally not be used by the
workforce. This problem includes the use of jargon and acronyms in communication between
groups. Worker participation in the roll-out design may avert such shortcomings, and lead to
solutions such as multilingual instructions and guidelines, a wider use of symbols and
pictograms, and the selection of simple language. The wider approach to worker participation in
the plan will produce benefits in terms of “buy-in” and acceptance of the plan’s goals and
approaches.
The review process, or safety programme audit, should be repeated on a regular (annual) basis

5. and will form the basis for 3-year rolling (or cyclical) plans. These plans will establish the future
direction of the programme and provide the impetus for continual improvement, even in the face
of changing production and process systems.
Continuous Improvement
Successful safety programmes do not remain static, but change to reflect changes in both
corporate and social environments. Equally, successful programmes avoid dramatic but
unachievable goals. Instead, a philosophy of continuous improvement and of continually rising
standards is a key approach. The annual 3-year rolling plan is a good way to achieve that. Each
year, the plan identifies broad goals and estimates with respect to likely costs and benefits that
will develop over the next 3-year period. This will automatically provide for adaptation and
continued improvement. As such plans are to be reviewed by management each year, an
additional benefit will be that the objectives of the safety function are continuously aligned with
corporate objectives.
Conclusion
The implementation of the safety programme must reflect its being an integral component of the
management of the enterprise. Success would depend on clearly identifying the responsibilities
of the various levels of management. The participation of workers in the implementation
programme, and particularly the roll-out plan, is likely to produce benefits in the widespread
adoption of the plan. The roll-out plan is a document which identifies the necessary activities, the
timing of those activities and the responsibility for implementing each activity. The components
of each activity—whether training, development of a working procedure or education—must be
described in a way that is unambiguous to all levels of the enterprise. The final stage in the roll-
out plan is to ensure that a continuous improvement cycle can occur by the installation of a
safety programme audit on at least an annual basis.