Chapter 8.4, Problem 5E

To determine

To determine whether the given function is even, odd, or neither.

  $f\left(x\right)=4x+3$

Answer to Problem 5E

Neither.

Explanation of Solution

Given:

  $f\left(x\right)=4x+3$

Concept Used:

• A function is even if it satisfies the property: $f\left(-x\right)=f\left(x\right)$ .
• A function is odd if it satisfies the property: $f\left(-x\right)=-f\left(x\right)$ .
• And if a function does not satisfy either of above property then it is neither even nor odd.

Calculation:

In order to determine whether the given function is even, odd, or neither.

  $f\left(x\right)=4x+3$

Find relation between $f\left(-x\right),\text{ and }f\left(x\right)$ .

As,

  $\begin{array}{c}f\left(-x\right)=4\left(-x\right)+3\\ =-4x+3\end{array}$

Now,

  $f\left(-x\right)\ne f\left(x\right)\text{ and }f\left(-x\right)\ne -f\left(x\right)$

Thus, the given function does not satisfy the property of being odd or even.

Thus, the given function is neither odd nor even.