SOLUTION: Show all work: f(x)=8x-32 and g(x)=1/8x+32 Is f(x) the inverse of g(x) I missed this week in class and have no clue what this means or how to solve.

Algebra ->  Inverses -> SOLUTION: Show all work: f(x)=8x-32 and g(x)=1/8x+32 Is f(x) the inverse of g(x) I missed this week in class and have no clue what this means or how to solve.      Log On


   

Question 286349: Show all work: f(x)=8x-32 and g(x)=1/8x+32
Is f(x) the inverse of g(x)
I missed this week in class and have no clue what this means or how to solve.
Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
To find the inverse of the function g(x), we will first rewrite it so that g(x)=y:
g(x)=(1/8)x+32
y=%281%2F8%29x%2B32
An inverse function is simply one where the x and y values have been swapped. That means anywhere where there is an x, make it y, and anywhere you see a y, make it an x.
Step 1: swap the y and x values.
y=%281%2F8%29x%2B32
x=%281%2F8%29y%2B32
Now rearrange the equation so that y is isolated.
x-32=(1/8)y
Multiply both sides by 8:
8x-256=y
The inverse of g(x) is y=8x-256
f(x)=8x-32, so no, the inverse of g(x) is NOT equal to f(x)