Question

Determine whether the functions f(x) and g(x) are inverse functions.

f(x) = x-9. g(x) = x +9

no
yes

Answer 1

Yes

They are inverse functions

Explanation:

If two functions f(x) and g(x) are inverses of each other then
f(g(x)) = x and

g(f(x)) = x

We have f(x) = x - 9 and g(x) = x + 9

f( g(x) ) can be found by substituting the expression for g(x) for every x occurrence in f(x)

f( (g(x) ) = (x + 9) - 9 = x

g( f(x) ) = (x - 9) + 9 = x

So indeed f(x) and g(x) are inverses of each other