Operations on Functions

1. GENERAL MATHEMATICS
ONE-TO-ONE FUNCTION / INVERSE FUNCTION

2. ONE-TO-ONE FUNCTION
 function for which every element of the range
of the function corresponds to exactly one
element of the domain. One-to-one is often
written 1-1.
 NOTE: y = f(x) is a function if it passes the
vertical line test and the horizontal line test.

3. GRAPHING ONE-TO-ONE FUNCTION
Construct a table of values. Simply choose a
number for x
Solve for the corresponding value of y.
Plot the points on the graph.
Connect the points.

4. INVERSE FUNCTION
 function obtained by switching the x and y variables in a
function. The inverse of function f is written f -1
 NOTE: The new relation obtained by reversing the x and y
values of a function is not necessarily a function itself. The
new relation is only a function if the original function is
one-to-one function.

5. INVERSE FUNCTION
 Change f(x) to y
Interchange x and y
Solve y in terms of x
Change y to f -1

6. EXAMPLE
 For each of the following functions find the inverse of the
function.
a. f(x)=6x+15
b. h(x)=3−29x
c. h x =
1+9𝑥
4−𝑥
d. R(x)=x3+6

7. QUIZ 4
Find the inverse for each function. Show all necessary solution.
1. 𝑧 𝑥 = 4𝑥 − 10
2. 𝑑 𝑥 =
8−12𝑥
3𝑥+2
3. 𝑟 𝑥 =
5𝑥+1
𝑥−1
4. 𝑏 𝑥 =
3𝑥 − 5
3𝑥 + 5
5. 𝑠 𝑥 = 𝑥5
− 4