Decide whether or not the functions are inverses of each other.
-f(x)= 9x - 6, g(x)=
A)No
B)Yes

Question

Decide whether or not the functions are inverses of each other.
-f(x)= 9x - 6, g(x)= 
A)No 
B)Yes

Quizplus · Accepted Answer

To determine if two functions are inverses of each other, we need to see if the composition of the two functions in either order equals the input. That is, we need to see if f(g(x))=x or g(f(x))=x for all values of x.
 
For this problem, let's first find g(f(x)):
g(f(x))=11(9x-6)+2=99x-64
 
Now, let's try to find f(g(x)):
f(g(x))=9(11x+2)-6=99x+12
 
Since f(g(x)) does not equal x, and g(f(x)) does not equal x, these two functions are not inverses of each other. In order for two functions to be inverses of each other, the composition of the functions (f(g(x)) and g(f(x))) should give the input back. 
However, if we try to find the composition of f(g(x)), we get:
f(g(x)) = f(11e^x - 6) = 9(11e^x - 6) - 6 = 99e^x - 60
This is not equal to x, so the functions are not inverses of each other.

Decide Whether or Not the Functions Are Inverses of Each