Q. 27 - Precalculus Enhanced with Graphing Utilities

Question

If $f\left(x\right)=\left\{\begin{array}{l}2x-4 if -1\le x\le 2\\ x^3-2 if 2<x\le 3\end{array}\right.$

Find: (a) $f\left(0\right)$  (b) $f\left(1\right)$  (c)  $f\left(2\right)$  (d) $f\left(3\right)$

Step-by-Step Solution

Answer

(a) $-4$

(b)  $-2$

(c)  $0$

(d)  $25$

Step 1.Given information

The given function $f\left(x\right)=\left\{\begin{array}{l}2x-4 if -1\le x\le 2\\ x^3-2 if 2<x\le 3\end{array}\right.$

Step 2.Find the value of f ( 0 )

When $x=0$, the equation for is given by $f\left(x\right)=2x-4$.

Replace $x$ with $0$ in the function and simplify

$$\begin{gathered} f\left(0\right)=2\left(0\right)-4 \\ =-4 \end{gathered}$$

Therefore,the value of $f\left(0\right)=-4$.

Step 3.Find the value of f ( 1 )

When $x=1,$ the equation for is given by $f\left(x\right)=2x-4$

Replace $x$ with $1$ in the function and simplify.

$$\begin{gathered} f\left(1\right)=2\left(1\right)-4 \\ =2-4 \\ =-2 \end{gathered}$$

Therefore,the value of $f\left(1\right)=-2$

Step 4.Find the value of f ( 2 )

When $x=2,$ the equation for is given by $f\left(x\right)=2x-4$

Replace $x$ with $2$ in the function and simplify

$$\begin{gathered} f\left(2\right)=2\left(2\right)-4 \\ =4-4 \\ =0 \end{gathered}$$

Therefor,the value of $f\left(2\right)=0$

Step 5.Find the value of f ( 3 )

When $x=3,$ the equation for is given by $f\left(x\right)=x^3-2$

Replace $x$ with $3$ in the function and simplify

$$\begin{gathered} f\left(3\right)={\left(3\right)}^3-2 \\ =27-2 \\ =25 \end{gathered}$$

Therefore,the value of $f\left(3\right)=25$