Question

Determine if the function is even, odd, or neither
$f\left(x\right)=-4x^5+7x^3$

• A. Even
• B. Odd
• C. Neither
• D. Both

Answer 1

Answer: (B)

Odd

Given : $f\left(x\right)=-4x^5+7x^3$

To check, whether the function is odd or even

The function $f$ is even, if $f(-x)=f\left(x\right)$

$f$ is odd, if $f(-x)=-f\left(x\right)$

Consider $f\left(x\right)$

$=-4(-x{)}^5+7(-x{)}^3$

$=4x^5-7x^3$ ........... $[\because (-x{)}^n=-x^n,ifnisodd]$

$=-(-4x^5+7x^3)$

$=-f\left(x\right)$

$\therefore f(-x)=-f\left(x\right)$

Hence, $f$ is odd.