- SlideShare.net is a popular presentation and document sharing platform owned by LinkedIn that is usually used for business purposes. It allows users to upload presentations and documents up to 300MB in size but does not enable making or designing presentations. - The document discusses a commissions problem where monthly earnings are ₱10,000 plus 5% commission on total sales. It represents this as a function f(x)=10,000+0.05x and proves that the inverse function f^-1(x)=x-10,000/0.05. - It then uses the inverse function to determine that if monthly earnings are ₱15,000, total sales for the month must be

1. SLIDESHARE.NET
 is a popular presentation and document sharing platform owned by LinkedIn.
 Usually used for business
 Free and very easy to use
 CANNOT make and design presentations
 Maximum upload size is 300mb

3. GROUP 5 – COMMISSIONS PROBLEM

4.  We need to look at the given:
10000 – Monthly Earnings
5% commission from total sales
Assume the total monthly earnings as y
And total sales as x
 Add 10000 to the total sales, and multiply x by 5% or 0.05
y = 10000 + 0.05x
 Since this is a function, we can represent this as:
f(x) = 10000 + 0.05x

5. GIVEN: f(x) = 0.05x + 10000
PROVE: x1 = x2
Substitute x1 and x2
Assume x1 = x2
A.P.E
D.P.E
f(x1) = 10000 + 0.05x1
f(x2) = 10000 + 0.05x2
0.05x1 = 0.05x2
10000 + 0.05x1 = 10000 + 0.05x2
x1 = x2

6.  Interchange the x and y variables
f(x) = 10000 + 0.05x
y = 10000 + 0.05x
x = 10000 + 0.05y
 Add -10000 to both sides
x-10000 = 0.05y
 Solve for y in terms of x and interchange y into inverse notation
f-1(x) = x-10000
0.05

7. Graph and Properties of The Functions
y = 10000 +0.05x
y = x-10000
0.05

8. Properties
PROVE: f-1(x)= x – 10000
0.05
is the inverse of f(x)= 0.05x + 10000
(f o g) (x)= (g o f) (x) = x
Where f(x) is 0.05x + 10000
and g(x) is x – 10000
0.05

9. (f(g(x))= x
f(g(x)) = 0.05(x-10000) + 10000
0.05
f(g(x)) = x – 10000 + 10000 = x
(g(f(x))= x
g(f(x)) = (0.05x + 10000) – 10000
0.05
g(f(x)) = x + 200000 – 200000 = x

10.  If total earnings for the month is ₱15000,
Find the total sales for the month
 Utilize inverse function
f-1(x) = x -10000
0.05
 Substitute 15000
f-1(15000) = 15000 -10000
0.05
 Simplify
f-1(15000) = 100000
The total sales for the month is ₱100000