Question

If $f\left(x\right)=\left\{\begin{array}{l}{x}^{3}if-2\le x<1\\ 3x+2if1\le x\le 4\end{array}\right.$

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

Short answer

(a)$-1$

(b)$0$

(c)$5$

(d)$11$

Step-by-step solution

Step 1.Given information

/the given function$f\left(x\right)=\left\{\begin{array}{l}{x}^{3}if-2\le x<1\\ 3x+2if1\le x\le 4\end{array}\right.$

Step 2.Find the value of f(-1)

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

localid="1645803083162" $$\begin{gathered} f(-1)={(-1)}^3 \\ =-1 \\ Therefore,thevalueoff(-1)=-1 \end{gathered}$$

Step 3.Find the value of f(0)

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

localid="1645802558614" $$\begin{gathered} f\left(0\right)={\left(0\right)}^3 \\ =0 \end{gathered}$$

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$f\left(3\right)=11$