Question

The function $y=f\left(\right|x\left|\right)$ is symmetric about the line

• A. $x=0$
• B. $y=0$
• C. $y=x$
• D. $y=-x$

Answer 1

The correct option is A $x=0$

In the function $y=f\left(\right|x\left|\right)$,
$x$ can take any value.
But $\left|x\right|$ will give same output for positive and negative values of x.
$\Rightarrow f\left(x\right)=f(-x)$
Hence, the graph will be symmetric about y-axis or the line x = 0.