Question

If $x$ is a real number then $$\begin{gathered} \left|x\right|=xifx\ge 0 \\ \left|x\right|=\_\_\_\_\_\_\_ifx<0 \end{gathered}$$

Answer 1

Modulus function:

A modulus function is a function that gives the absolute value of a number or variable. It produces the magnitude of the number of variables.

Explanation:

We know that the modulus of a function is always positive.

Given that, $\left|x\right|=xforx\ge 0$

If $x<0$ then the value of $x$ is negative but $\left|x\right|$ should be always positive.

Hence, we will take $\left|x\right|=-xforx<0$

Here, the negative sign and the negative value of $x$ will make $\left|x\right|>0$

Conclusion:

Hence, $$\begin{gathered} \left|x\right|=xifx\ge 0 \\ \left|x\right|=-xifx<0 \end{gathered}$$