Question

If the range of f(x) is $(-(\infty ,\infty )$, then the range of g(x) = $\frac{1}{\sqrt{f\left(x\right)}}$ is

• A. (-,)
• B. (0,)
• C. (-,0)
• D. None of these

Answer 1

The correct option is B

(0,)

$\sqrt{f\left(x\right)}$ is greater than or equal to zero . When $\sqrt{f\left(x\right)}$ tends ( approaches ) to zero,

$\frac{1}{\sqrt{f\left(x\right)}}$ will tends to $\infty$ . As $\sqrt{f\left(x\right)}$ tends to $\infty$ , $\frac{1}{\sqrt{f\left(x\right)}}$ will tends to zero,

So the range will be (0,$\infty$)