Question

Evaluate the piecewise defined function at the indicated values.

$\begin{array}{l}f\left(x\right)=\left\{\begin{array}{cc}5& \text{if\hspace{0.33em}}x\le 2\\ 2x-3& \text{if\hspace{0.33em}}x>2\end{array}\right.\\ f\left(-3\right),f\left(0\right),f\left(2\right),f\left(3\right),f\left(5\right)\end{array}$

Short answer

The required values are $f\left(-3\right)=5,f\left(0\right)=5,f\left(2\right)=5,f\left(3\right)=3,f\left(5\right)=7$.

Step-by-step solution

Step 1. Given Information.

The given piecewise function is:

$f\left(x\right)=\left\{\begin{array}{cc}5& \text{if\hspace{0.33em}}x\le 2\\ 2x-3& \text{if\hspace{0.33em}}x>2\end{array}\right.$

Here,$f\left(x\right)=5$ when$x\le 2$ and$f\left(x\right)=2x-3$ when $x>2$.

Step 2. Solve for first value.

Since $-3\le 2$, therefore substitute$x=-3$ in $f\left(x\right)=5$.

$f(-3)=5$

Step 3. Solve for second value.

Since $0\le 2$, therefore substitute$x=0$ in $f\left(x\right)=5$.

role="math" localid="1644521009344" $f\left(0\right)=5$

Step 4. Solve for third value.

Since $2\le 2$, therefore substitute $x=2$in $f\left(x\right)=5$.

$f\left(2\right)=5$

Step 5. Solve for fourth value.

Since $3>2$, therefore substitute$x=3$ in $f\left(x\right)=2x-3$.

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

Step 6. Solve for fifth value.

Since $5>2$, therefore substitute$x=5$ in $f\left(x\right)=2x-3$.

role="math" localid="1644520861250" $$\begin{gathered} f\left(5\right)=2\left(5\right)-3 \\ =10-3 \\ =7 \end{gathered}$$

Thus, the required values are $f\left(-3\right)=5,f\left(0\right)=5,f\left(2\right)=5,f\left(3\right)=3,f\left(5\right)=7$.