Question

Which among the following function graph(s) are symmetrical about $y-$axis?

• A. $f_1\left(x\right)=x\left(\frac{7^x-1}{7^x+1}\right)$
• B. $f_2\left(x\right)=x^2+2$
• C. $f_3\left(x\right)=\frac{1}{x},x\ne 0$
• D. $f_4\left(x\right)=x^3+3$

Answer 1

Answer: (A), (B)

$f_2\left(x\right)=x^2+2$

If a graph of a function has to be symmetrical about $y-$axis, then it has to be an even function.
Now,
$f_1(-x)=f_1\left(x\right)\Rightarrow f_1\left(x\right)$ is even function
$f_2(-x)=f_2\left(x\right)\Rightarrow f_2\left(x\right)$ is even function
$f_3(-x)=-f_3\left(x\right)\Rightarrow f_3\left(x\right)$ is odd function
$f_4(-x)=-x^3+3\Rightarrow f_3\left(x\right)$ is neither even nor odd function.