Chapter 1.3, Problem 92E

(a)

To determine

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

Answer to Problem 92E

  $f\left(x\right)=x\sqrt{3+x}$ , is an odd function.

Explanation of Solution

Given: Function is

  $f\left(x\right)=x\sqrt{3+x}$

Calculation:

  $\begin{array}{l}f\left(x\right)=x\sqrt{3+x}\\ f\left(-x\right)=-x\sqrt{3+\left(-x\right)}\\ =-x\sqrt{3-x}\\ \because f\left(-x\right)\ne -f\left(x\right)\end{array}$

and

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

So, function neither even nor odd function.

(b)

To determine

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

Answer to Problem 92E

  $f\left(x\right)=x\sqrt{3+x}$ ,neither odd nor even.

Explanation of Solution

Given: Function is

  $f\left(x\right)=x\sqrt{3+x}$

Observation:

Graph of function is

  

Since graph of function is neither symmetric about origin nor symmetric about $x$ axis.So function is neither odd nor even.

(c)

To determine

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

Answer to Problem 92E

  $f\left(x\right)=x\sqrt{3+x}$ ,neither odd nor even.

Explanation of Solution

Given: Function is

  $f\left(x\right)=x\sqrt{3+x}$

Calculation:

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

  

From table

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

and

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

so function is neither odd nor even.