Question

I need help with question a and b

Answer 1

Solving for part A

$f(x) = x^{2} \;\;and\;\; g(x) = \frac{1}{x^{3}} \\\\f(g(x)) = (\frac{1}{x^{3}})^{2} =\frac{1}{x^{6}}$

Domain of composition: x ≠ 0 i.e. Domain is the set of "Real numbers excluding number 0".

Solving for part B

$f(x) = \frac{x}{x-2}\;\;and\;\;g(x) =\frac{3}{x} \\\\f(g(x))=\frac{\frac{3}{x}}{\frac{3}{x}-2}=\frac{\frac{3}{x}}{\frac{3-2x}{x}} =\frac{3}{3-2x}\\\\ Domain:\;3-2x\neq 0 \;\;OR\;\;x\neq \frac{3}{2}$