Question

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

Answer 1

f(g(x)) = (-3x - 7) - 7 (-3x - 7 ) + 3
------- / --------
(x - 1) ( x - 1)

convert the numerator and denominator to a single fraction
then invert the second fraction and multiply

Answer 2

(x-1)(-3x-7)-7/(x-1)(-3x-7)+3?

Answer 3

No you need to multiply through by (x- 1) so we get
-3x - 7 - 7(x - 1) -3x - 7 + 3(x - 1)
--------------- / --------------
x - 1 x - 1

Answer 4

Simplify both numerators then in ver and multiuply

the ( x - 1) will cancel out

Answer 5

I got that but now I don't know what to do.

Answer 6

they simplify to

-10x -10
------ / -----
(x - 1) (x - 1)

now its easy to show that this t is = x