Q. 26 - Precalculus Enhanced with Graphing Utilities

Question

If $f\left(x\right)=\left\{\begin{array}{l}-3x if x<-1\\ 0 if x=-1\\ 2x^2+1 if x>-1\end{array}\right.$

Find: (a)  $f(-2)$  and   (b) $f(-1)$    (c) $f\left(0\right)$

Step-by-Step Solution

Answer

(a)  $6$

(b)  $0$

(c)  1

Step 1.Given information

The given function $f\left(x\right)=\left\{\begin{array}{l}-3x if x<-1\\ 0 if x=-1\\ 2x^2+1 if x>-1\end{array}\right.$

Step 2. Finding the value of f ( - 2 )

We observe that when $x=-2$ the equation for $f$ is given by $f\left(x\right)=-3x$

Substitute $-2$ for $x$ in the function and evaluate

$$\begin{gathered} f(-2)=-3(-2) \\ = 6 \end{gathered}$$

Thus,the value of $f(-2)$ is $6$.

Step 3.Finding the value of f ( - 1 )

We observe that when $x=-1$ the equation for $f$  is given by $f\left(x\right)=0$

$f(-1)=0$

Thus,the value of $f(-1)$is $0$

Step 4. Finding the value of f ( 0 )

When $x=0$ the the equation is.Evaluate

$$\begin{gathered} f\left(0\right)=2x^2+1 \\ =2\left(0\right)+1 \\ =1 \end{gathered}$$

Thus,the value of $f\left(0\right)$ is $1$.