Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x)=(x-8)/(x+7) and g(x)=(-7x-8)/(x-1)

Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. 
f(x)=(x-8)/(x+7) and g(x)=(-7x-8)/(x-1)

anonymous · Answer

no one wants to do this algebra, because it is a real pain

anonymous · Answer

That's not the right attitude to get a problem done now is it? @satellite73

anonymous · Answer

have fun

anonymous · Answer

$$f(x)=\frac{x-8}{x+7}$$ 
$$g(x)=\frac{-7x-8}{x-1}$$

anonymous · Answer

$$f\circ g(x)=f\left(\frac{-7x-8}{x-1}\right)$$
$$=\frac{\frac{-7x-8}{x-1}-8}{\frac{-7x-8}{x-1}+7}$$

anonymous · Answer

clear the compound fraction by multiplying top and bottom by $x-1$
use parentheses and do the algebra carefully

anonymous · Answer

when you do it there will be an orgy of cancellation the likes of which is usually unseen and you will be left with only $x$

anonymous · Answer

Thank you for your help @satellite73 I appreciate it, have a good night.

anonymous · Answer

you too 
good luck with this one