Q. 28 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

(a) $-1$

(b) $0$

(c) $5$

(d) $11$

Step 1.Given information

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

Step 2.Find the value of f ( - 1 )

When $x=-1$, the equation for is given by $f\left(x\right)=x^3$

$$\begin{gathered} f(-1)={(-1)}^3 \\ =-1 \\ Therefore,the value of f(-1)=-1 \end{gathered}$$

Step 3.Find the value of f ( 0 )

When $x=0,$ the equation for is given by $f\left(x\right)=x^3$

$$\begin{gathered} f\left(0\right)={\left(0\right)}^3 \\ =0 \end{gathered}$$

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

Step 4.Find the value of f ( 1 )

When $x=1$ the equation for is given by $f\left(x\right)=3x+2$

$$\begin{gathered} f\left(1\right)=3\left(1\right)+2 \\ =3+2 \\ =5 \end{gathered}$$

Therefore,the value of $f\left(1\right)=5$ 

Step 5.Find the value of f ( 3 )

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

$$\begin{gathered} f\left(3\right)=3\left(3\right)+2 \\ =9+2 \\ =11 \end{gathered}$$

Therefore,the value of $f\left(3\right)=11$