Chapter 2.4, Problem 27AYU

If $f(x)=\{\begin{array}{cc}2x+4& if-3\le x\le 1\\ x^3-1& if1<x\le 5\end{array}$ find :

$f(-2)$

(b) $f(0)$

(c) $f(1)$

(d) $f(3)$

To determine

The value of $f(-2)$ where the function is $f(x)=\{\begin{array}{l}2x+4\text{if -3}\le x\le \text{1}\\ x^3-1\text{if 1< }x\le 5\end{array}$.

Answer to Problem 27AYU

Solution:

The value of $f(-2)$ is 0.

Explanation of Solution

Given Information:

The function, $f(x)=\{\begin{array}{l}2x+4\text{if -3}\le x\le \text{1}\\ x^3-1\text{if 1< }x\le 5\end{array}$

Explanation:

In $f\left(-2\right)$, $x=-2<0$.

Observe that for $\text{-3}\le x\le \text{1}$, $f\left(x\right)=2x+4$.

Then, to find the value of $f(-2)$, plug in $x=-2$ in $f\left(x\right)=2x+4$.

$\Rightarrow f(-2)=2\left(-2\right)+4$

$=-4+4$

$=0$

Hence, the value of $f(-2)$ is 0.

To determine

The value of $f(0)$ where the function is $f(x)=\{\begin{array}{l}2x+4\text{if -3}\le x\le \text{1}\\ x^3-1\text{if 1< }x\le 5\end{array}$

Answer to Problem 27AYU

Solution:

The value of $f\left(0\right)$ is 4.

Explanation of Solution

Given Information:

The function, $f(x)=\{\begin{array}{l}2x+4\text{if -3}\le x\le \text{1}\\ x^3-1\text{if 1< }x\le 5\end{array}$

Explanation:

In $f\left(0\right)$, $x=0$.

Observe that for $\text{-3}\le x\le \text{1}$, $f\left(x\right)=2x+4$.

Then, to find the value of $f(0)$, plug in $x=0$ in $f\left(x\right)=2x+4$.

$\Rightarrow f(0)=2\left(0\right)+4$

$=0+4$

$=4$

Hence, the value of $f\left(0\right)$ is 4.

To determine

The value of $f(1)$ where the function is $f(x)=\{\begin{array}{l}2x+4\text{if -3}\le x\le \text{1}\\ x^3-1\text{if 1< }x\le 5\end{array}$.

Answer to Problem 27AYU

Solution:

The value of $f\left(1\right)$ is 6.

Explanation of Solution

Given Information:

The function, $f(x)=\{\begin{array}{l}2x+4\text{if -3}\le x\le \text{1}\\ x^3-1\text{if 1< }x\le 5\end{array}$

Explanation:

In $f\left(1\right)$, $x=1$.

Observe that for $\text{-3}\le x\le \text{1}$, $f\left(x\right)=2x+4$.

Then, to find the value of $f(1)$, plug in $x=1$ in $f\left(x\right)=2x+4$.

$\Rightarrow f(1)=2\left(1\right)+4$

$=2+4$

$=6$

Hence, the value of $f\left(1\right)$ is 6.