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) = -7 x - 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) = -7 x - 8 / x -1.

anonymous · Answer

lots of ugly algebra ending in a raft of cancellation

anonymous · Answer

$$f(x)=\frac{x-8}{x+7}$$ replace $x$ by $\frac{-7x-8}{x-1}$ and get 
$$f(f^{-1}(x))=\frac{\frac{-7x-8}{x-1}-8}{\frac{-7x-8}{x-1}+7}$$

anonymous · Answer

multiply top and bottom by $x-1$ to clear the compound fraction
then there will be a whole slew of cancellation and you should end up only with $x$ if the inverse is correct

anonymous · Answer

I dont understand it still I see what you are trying to do but the print is small on my computer. Can you you do it like one thing at a time ?

anonymous · Answer

let me make it larger

anonymous · Answer

Thanks

anonymous · Answer

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

anonymous · Answer

So what would be left I think I got it

anonymous · Answer

if it is all correct, you should be left only with $\large x$

anonymous · Answer

ok I got it thanks

anonymous · Answer

yw