Question

Which of the following is true regarding the symmetry of the function:$f\left(x\right)=x^5+x^3+3$

• A. $f\left(x\right)=c$
• B. Symmetric about x-axis
• C. Its an odd function
• D. None of these

Answer 1

The correct option is D None of these

The graph is shown in the image.

$f\left(x\right)=x^5+x^3+3$ .....equ($1$)

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

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

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

$f(-x)=(-x{)}^5+(-x{)}^3+3$

$f(-x)=-x^5-x^3+3$

Hence, $f\left(x\right)\ne f(-x)$ or $f\left(x\right)\ne -f\left(x\right)$ ,hence function is neither even nor odd function

$concept$ --

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

Because given function is neither odd nor even function, hence it is not symmetric about any of the axis.