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

f(g(x)) means substitute f(x) for the x in f(x)
\[f(g(x)) = (\sqrt{3+x})^2-3\]
do the reverse to get g(f(x))
\[g(f(x))=\sqrt{3+(x^2-3)}\]
Simplify them both. If you get "x" for both the functions are inverses