Question

If $f\left(x\right)=\left\{\begin{array}{l}2x-4if-1\le x\le 2\\ x^3-2if2<x\le 3\end{array}\right.$

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

Short answer

(a)$-4$

(b)$-2$

(c) $0$

(d) $25$

Step-by-step solution

Step 1.Given information

The given function$f\left(x\right)=\left\{\begin{array}{l}2x-4if-1\le x\le 2\\ x^3-2if2<x\le 3\end{array}\right.$

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

role="math" localid="1645801017731" $$\begin{gathered} f\left(3\right)={\left(3\right)}^3-2 \\ =27-2 \\ =25 \end{gathered}$$

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