Question

Can someone help me please

Answer 1

If the functions are inverses, then f(g(x)) = x.

A.

`\displaystyle f(g(x))=f\left((3x+1)/(3)\right)=(1)/((3x+1)/(x)-3)\\\\=(1)/(\left((3x+1-3x)/(x)\right))=(1)/(\left((1)/(x)\right))=x`

The functions are inverses of each other.

B. The domain of f(x) = x≠3. The domain of g(x) is x≠0.

The domain of f(g(x)) is (-∞, 0) ∪ (0, ∞).

The domain of g(f(x)) is (-∞, 3) ∪ (3, ∞).