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

Question

F(x)= (x-7)/(x+3)

G(x)= (-3x-7)/ (x-1) 

Answer 1

For F(G(X)), plug in all of G(x) for the x values in F(x). 

That would look like:

F(G(x)) = ([(-3x-7)/(x-1)] - 7) / ([(-3x-7)/(x-1)] + 3)

multiply the -7 and the 3 by (x-1) so that both the numerator and denominator of the big fraction have denominators of (x-1).

both denominators cancel out then.

this becomes:

(-10x)/-10 => x

So the first one is true. 

 

Follow the same steps for g(f(x)). 

Plug in all of (f(x)) for where g(x) has x's. then manipulate to get the answer x, if you do get just x, then both can be confirmed true.