Question

For $0\le x\le 1$, the function $f\left(x\right)=\left|x\right|+\left|x-1\right|$ is -

• A. Monotonically increasing
• B. Monotonically decreasing
• C. Constant function
• D. Identity function

Answer 1

Answer: (C)

Constant function

$given0\le x\le 1then-1\le x-1\le 0$

$f\left(x\right)=\mid x\mid +\mid x-1\mid$

In the given interval $x$ is positive and $x-1$ is negative

so $f\left(x\right)=x+1-x=1$

$\therefore f\left(x\right)$ is constant function