Question

Which of the following is true regarding the symmetry of the function:$f\left(x\right)=x^4+x^2+3$?

• A. $f\left(x\right)=f(-x)$
• B. $f\left(x\right)=-f(-x)$
• C. Its an even function
• D. Symmetric wrt y-axis

Answer 1

Answer: (A), (C), (D)

The correct options are
A $f\left(x\right)=f(-x)$
C Its an even function
D Symmetric wrt y-axis

The graph is shown in the image.

$f\left(x\right)=x^4+x^2+3$ .....equ($1$)

If $f\left(x\right)=f(-x)$,then function is called even function

If $f\left(x\right)=-f(-x)$,then function is called odd function

Put $x=-x$ in equ($1$)

$f(-x)=(-x{)}^4+(-x{)}^2+3$

$f(-x)=x^4+x^2+3$

Hence, $f\left(x\right)=f(-x)$, hence function is even function

$concept$ --

Every EVEN function are symmetric about $Y$-axis and every ODD function are symmetric about $X$-axis

Because given function is even function, hence it is symmetric w.r.t to $Y$-

axis