Question

$f\left(x\right)=0,$ when $x=0$ and $x-3$, when $x>0$. The function $f\left(x\right)$ is

• A. Increasing when $x\ge 0$
• B. Strictly increasing when $x>0$
• C. Strictly increasing at $x=0$
• D. Not continuous at $x=0$ and so it is not increasing when $x>0$

Answer 1

The correct option is B

Strictly increasing when $x>0$

Explanation for the correct option:

Draw the graph of $y=x-3$:

Given, $f\left(x\right)=0,$ when $x=0$ and $x–3$, when $x>0$

$\Rightarrow$ $f\left(x\right)=\left\{\begin{array}{ll}0,& x=0\\ x-3,& x>0\end{array}\right.$

It is clear from the graph that $f\left(x\right)$ is strictly increasing when $x>0$

Hence, Option ‘B’ is Correct.