Chapter 1, Problem 53CR

To determine

Tostate:State whether the given function is even, odd or neither.

Answer to Problem 53CR

The given function is neither even nor odd.

Explanation of Solution

Given information:The given function is $f\left(x\right)=3x^{\frac{5}{2}}$

A function $y=f\left(x\right)$ is said to be an even function if the graph of the function is symmetrical about y-axis. Algebraically, $y=f\left(x\right)$ is even if $f\left(-x\right)=f\left(x\right)$ for all x in the domain.

Similarly, a function $y=f\left(x\right)$ is said to be an odd function if the graph of the function is symmetrical about origin. Algebraically, $y=f\left(x\right)$ is even if $f\left(-x\right)=-f\left(x\right)$ for all x in the domain.

Here the graph of the function is $f\left(x\right)=3x^{\frac{5}{2}}$

We have

  $\begin{array}{c}f\left(-x\right)=3{\left(-x\right)}^{\frac{5}{2}}\\ =3{\left\{{\left(-x\right)}^5\right\}}^{\frac{1}{2}}\\ =3{\left\{-x^5\right\}}^{\frac{1}{2}}\\ \ne f\left(x\right)\end{array}$

As square root of negative number is not define.

Therefore, the given function is neither even nor odd.

The graph of the function is shown below