Question

Are F(x) and G(x) inverse functions across the domain [3,+ ∞)?

F(x)=√x-3+8
G(x) = (x+8)²-3

Answer 1

A

Step-by-step explanation:

For functions to be inverse, it must be true that

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

But for F(G(x)) we have V(G(x) - 3) + 8

= V((x + 8) ^ 2 - 3 - 3) + 8

= V((x + 8) ^ 2 - 6) + 8

This -6 part should be cancelled out for functions to work out but we cannot do that, therefore F(x) and G(x) are not inverse.