Question

Find the domain of $f\left(x\right)=\frac{1}{\sqrt{x}}$,

• A. All real numbers
• B. All integers except zero
• C. All positive real numbers except zero
• D. All real numbers except zero

Answer 1

Answer: (C)

All positive real numbers except zero

$f\left(x\right)=\frac{1}{\sqrt{x}}$

The value of $x$ should not be $0$ and negative integer

when $x=0$

$f\left(x\right)=\frac{1}{\sqrt{0}}$ which is not definite

$x=-1$

$f\left(x\right)=\frac{1}{\sqrt{-1}}$ which is not a real number.

So the domain of $f\left(x\right)=\frac{1}{\sqrt{x}}$ is $(0,\infty )$.

All positive real number except zero.