Determine whether f and g are inverse functions by evaluatin

Determine whether f and g are inverse functions by evaluating f(g(x)) and g(f(x)). f(x)=x^2 + 2: domain [0,infinity) g(x) = x-2:domain [2,infinity) Evaluate f(g(x)). f(g(x)) = x Evaluate g(f(x)). g(f(x)) = x Are f(x) and g(x) inverses functions? Yes No

Solution

f(x)=x²+2

g(x)=(x-2)

a)fog

=f(g(x))

=((x-2))²+2

=x-2+2

=x

b)gof

=g(f(x))

=((x²+2)-2)

=x²

=x

f(g(x))=g(f(x))=x

yes g(x) and f(x) are inverse functions