Question

If $f\left(x\right)=a{x}^5+b{x}^3+cx+d$ is an odd function, then

• A. $a=0$
• B. $b=0$
• C. $c=0$
• D. $d=0$

Answer 1

The correct option is D $d=0$

For an Odd function
$f(-x)=-f\left(x\right)\Rightarrow a(-x{)}^5+b(-x{)}^3+c(-x)+d=-(a{x}^5+b{x}^3+cx+d)\Rightarrow a(-x{)}^5+b(-x{)}^3+c(-x)+d=-a{x}^5-b{x}^3-cx-d\Rightarrow 2d=0\Rightarrow d=0$