Question

The function $f\left(x\right)=\frac{1}{x};x>0$ on its domain is

• A. increasing
• B. decreasing
• C. constant
• D. information insufficient

Answer 1

Answer: (B)

decreasing

Given, $f\left(x\right)=\frac{1}{x}$
Therefore

$f^{\prime }\left(x\right)=\frac{-1}{x^2}$

The domain of the above function is $x>0$.

Therefore

$f^{\prime }\left(x\right)<0$

Hence $f\left(x\right)$ is a decreasing function.