Question

Which of the following function is a monotonic function?

• A. f(x) = Sin(x)
• B. $f\left(x\right)=\frac{1}{x^2}$
• C. $f\left(x\right)=x^3$
• D. f(x) = {x} ; where {} is the fractional part function.

Answer 1

The correct option is C

$f\left(x\right)=x^3$

A function is said to be monotonic if it's either non- increasing or non-decreasing.

$\frac{1}{x^2}$ increases in the interval $(-\infty ,0)$and decreases in the interval $(0,\infty )$. So, B is also not monotonic.

$f\left(x\right)=x^3$ is an example of monotonically increasing function. So, this is a monotonic function.

{x} increases from 0 to 1(never becomes 1) between two integers and then becomes 0 at the next integer. So, this is not monotonic as it changes its behaviour.