Question 57656
For g(x) to be an inverse of f(x), the following should be true:
g(f(x))=x.

g(f(x)) = {{{(10((8x+9)/8)-7)/8}}}
= {{{ (10/8)(x+9/8)-7/8}}}
={{{(10/8)x+(90/64)-(7/8)}}}
This simplifies to a linear equation in x {{{1.25x+.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(300,200,-2,20,-2,20,(8x+9)/8,(10x-7)/8, x)}}}