Question

Can someone help me please

Answer 1

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

A.

$\displaystyle f(g(x))=f\left(\frac{3x+1}{3}\right)=\frac{1}{\frac{3x+1}{x}-3}\\\\=\frac{1}{\left(\frac{3x+1-3x}{x}\right)}=\frac{1}{\left(\frac{1}{x}\right)}=x$

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, ∞).