Question

the functions f and g are given by $f(x) = \frac{1}{x}$ and $g(x) = \sqrt{x}$. what is the domain of the function h given by $h(x) = f(g(x))$ ?
a all real numbers
b all real numbers not equal to 0
c all real numbers greater than 0
d all real numbers greater than or equal to 0

Explanation:

Step1: Find \( h(x) \)

First, substitute \( g(x) \) into \( f(x) \). Given \( f(x)=\frac{1}{x} \) and \( g(x)=\sqrt{x} \), then \( h(x)=f(g(x)) = f(\sqrt{x})=\frac{1}{\sqrt{x}} \).

Step2: Determine domain of \( h(x) \)

For the square root function \( \sqrt{x} \), the radicand must be non - negative, so \( x\geq0 \). But in the denominator \( \sqrt{x}
eq0 \) (because division by zero is undefined), so \( x > 0 \).

Answer:

C. All real numbers greater than 0