Question

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

f(x) = x2 - 3 and g(x) = square root of quantity three plus x

Answer 1

I see a whole bunch of posts, but no indication of your attempts to solve them. I'll do one of them here:

f(g) = g^2-3 = (√(3+x))^2 - 3 = 3+x-3 = x
g(f) = √(f+3) = √(x^2-3+3) = √x^2 = x

However, note that √x^2 is not necessarily x.

If x = -3, √9 = 3, <b>not</b> -3!