Question

3) Using composition, determine if f(x) = x^2 + 2 and g(x) = x^2 - 2 are inverses.

4) Using composition, determine if f(x) = 2x + 4 and g(x) =1/2x -2 are inverses.

Answer 1

if f(g(x))=x and g(f(x))=x then they are inverse functionsf(g(x))=f(12x+2)f(g(x))=2(12x+2)−4f(g(x))=x+4−4=xg(f(x))=g(2x−4)g(f(x))=12(2x−4)+2g(f(x))=x−2+2=x⇒f(x) and g(x) are inverse functions

Answer 2

so in cas if are inverses what you need get using composition ?