SOLUTION: Determine whether the following functions are inverse. f(x) = (8x+9)/8 g(x) = (10x-7)/8 I am unable to solve.

Algebra ->  Functions -> SOLUTION: Determine whether the following functions are inverse. f(x) = (8x+9)/8 g(x) = (10x-7)/8 I am unable to solve.       Log On


   

Question 57656: Determine whether the following functions are inverse.
f(x) = (8x+9)/8
g(x) = (10x-7)/8
I am unable to solve.
Answer by hayek(51) About Me  (Show Source):
You can put this solution on YOUR website!
For g(x) to be an inverse of f(x), the following should be true:
g(f(x))=x.
g(f(x)) = %2810%28%288x%2B9%29%2F8%29-7%29%2F8
= +%2810%2F8%29%28x%2B9%2F8%29-7%2F8
=%2810%2F8%29x%2B%2890%2F64%29-%287%2F8%29
This simplifies to a linear equation in x 1.25x%2B.53125 and not simply x, so g(x) is not an inverse of f(x).
Another way to check is graphically. For g(x) to be an inverse, it should be symmetrical around y=x compared to f(x). As shown in this chart (where y=x is the blue line), g(x) is not symmetrical around around y=x.
graph%28300%2C200%2C-2%2C20%2C-2%2C20%2C%288x%2B9%29%2F8%2C%2810x-7%29%2F8%2C+x%29