Question

Help please :o)

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

Answer 1

\[f(x)=\frac{ x-7 }{x+3 } ; g(x)=\frac{ -3x-7 }{ x-1 }\]

Answer 2

\[\large \color{#CC0033}{f(x)=\frac{x-7}{x+3}};\qquad \color{#3366CF}{g(x)=\frac{-3x-7}{x-1}}\]

\[\large \color{#CC0033}{f(\color{#3366CF}{g(x)})}=\color{#CC0033}{\frac{\color{#3366CF}{g(x)}-7}{\color{#3366CF}{g(x)}+3}}\]

This is going to be rather messy plugging this all in :) lol\[\huge =\color{#CC0033}{\frac{\color{#3366CF}{\frac{-3x-7}{x-1}}-7}{\color{#3366CF}{\frac{-3x-7}{x-1}}+3}}\]

Answer 3

They want you to simplify it from there? D: Oh boy....

Answer 4

I think I figured it out:
f(x)=
0=x-7/x+3
x= -7/3

y=-7-7/-3+3
y=0

(0, -7/3)

g(x)=
0=-3x-7/x-1
0=-7/-2x-1
0=-7/-3

(-7/3, 0)

??? Maybe haha

Answer 5

Hmm <:o

Answer 6

Thanks for trying to help me though, I appreciate it :o)