Chapter 1.3, Problem 93E

(a)

To determine

To check function even, odd neither even nor odd algebraically.

Answer to Problem 93E

  $f\left(x\right)=4x^{2/3}$ , is an even function.

Explanation of Solution

Given: Function is

  $f\left(x\right)=4x^{2/3}$

Calculation:

  $\begin{array}{l}f\left(x\right)=4x^{2/3}\\ f\left(-x\right)=4x^{2/3}\\ \because f\left(-x\right)=f\left(x\right)\end{array}$

So, function is an even function.

(b)

To determine

To check function even, odd neither even nor odd graphically.

Answer to Problem 93E

  $f\left(x\right)=4x^{2/3}$ , is an even function.

Explanation of Solution

Given: Function is

  $f\left(x\right)=4x^{2/3}$

Observation:

Graph of function is

  

Since graph of function is symmetric about $y$ axis, so function is an evenfunction.

(c)

To determine

To check function even, odd neither even nor odd numerically.

Answer to Problem 93E

  $f\left(x\right)=4x^{2/3}$ , is an even function.

Explanation of Solution

Given: Function is

  $f\left(x\right)=4x^{2/3}$

Calculation:

Tables of values of $x,f\left(x\right)$ and $f\left(-x\right)$ is

  

From table

  $f\left(-x\right)=f\left(x\right)$

So, function is an even function.