Question

Determine the domain of the function (f*g)(x) where f(x)=1/x, g(x)=√2-5x

Answer 1

Answer:  (∞, 0) ∪ (0, 2/5)

               In other words, x is less than 2/5 but cannot include 0

Step-by-step explanation:

$f(x)\cdot g(x)=\dfrac{1}{x}\cdot\dfrac{1}{\sqrt{2-5x}}\\\\\\\text{The denominator cannot equal zero and must be a real number, so}\\x\neq 0\quad and\quad \sqrt{2-5x}>0\\\\\\(\sqrt{2-5x})^2>0^2\\.\quad 2-5x>0\\.\qquad -5x>-2\\\\.\qquad \quad x$