Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = 9x + 3 and g(x) =(x-3)/9 i did some of it just need someone to check it for me :O

Answer 1

i did this much but i think its wrong
f(g(x))=9(x^2+3/9)+3
g(f(x))=-3(9x^2+3)/9

Answer 2

If we substitute the function for the function, then we have:

f((3x + 5)/(1 - 2x)) = ((3x + 5)/(1 - 2x) - 5)/(2(3x + 5)/(1 - 2x) + 3) * (1 - 2x)/(1 - 2x)
==> (3x + 5 - 5(1 - 2x))/(6x + 10 + 3(1 - 2x))
==> (3x + 5 - 5 + 10x)/(6x + 10 + 3 - 6x)
==> 13x/13
==> x

g((x - 5)/(2x + 3)) = (3(x - 5)/(2x + 3) + 5)/(1 - 2(x - 5)/(2x + 3)) * (2x + 3)/(2x + 3)
==> (3x - 15 + 5(2x + 3))/(2x + 3 - 2x + 10)
==> (3x - 15 + 10x + 15)/13
==> 13x/13
==> x

Since f(g(x)) = g(f(x)) = x, f(x) and g(x) are invese of each other.

Answer 3

wow thx gaby :)

Answer 4

np :) good luck!!!