IM VERY CONFUSED ON HOW TO DO THIS PLEASE HELP
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x)=(x-7)/(x+3) and g(x)=(-3x-7)/(x-1)

Question

IM VERY CONFUSED ON HOW TO DO THIS PLEASE HELP
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. 
f(x)=(x-7)/(x+3) and  g(x)=(-3x-7)/(x-1)

anonymous · Answer

@robtobey

anonymous · Answer

@campbell_st

campbell_st · Answer

to find f(g(x))  just replace x in f(x) with g(x)   then do the algebra to see where you end up

campbell_st · Answer

so f(g(x)) is 

$$f(g(x)) = \frac{\frac{-3x -7}{x -1} - 7}{\frac{-3x -7}{x + 1} + 3}$$

campbell_st · Answer

oops I have thw wrong sign in the denominator it should be x - 1

anonymous · Answer

Refer to the attachment from Mathematica.

anonymous · Answer

haha yeah i just caught that. i understand that part i just dont know what to do after that

campbell_st · Answer

so I'd expect the next step is common denominators

$$f(g(x)) = \frac{\frac{(-3x -7) - 7(x -1)}{x -1}}{\frac{(-3x -7) + 3(x -1)}{x -1}}$$

then away you go

anonymous · Answer

oh ok thanks i think i got it from here

campbell_st · Answer

so just check.... my signs and things... 

but it is basically substitution, then getting common denominators and then simplifying and at least you are told the answer should be x. 

hope it helps