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

Question

f(x)=(x+4)/6

g(x)=6x-4

Answer 1

When you see x, you replace it with the expression you have in the argument. I replaced x in the call f(g(x)) with 6x-4 below.

Let try f(g(x)):

f(g(x)) = f(6x-4)

= [(6x-4) + 4]/6

= [6x]/6 = x.

You can work g(f(x)) similar way.

Here is the setup for you:

g(f(x)) =g( (x+4)/6 )

= ...