Question

Evaluate the function

a) $f(-2)$b) $f\left(3\right)$c) $f\left(a\right)$

$f\left(x\right)=x^2-5x+6$

Short answer

The function is $f\left(x\right)=x^2-5x+6$

a) To evaluate $f(-2)$, so we get$20$

b) To evaluate $f\left(3\right)$, so we get$0$

c) To evaluate $f\left(a\right)$, so we get$a^2-5a+6$

Step-by-step solution

Step 1. Given Information

We have the function

$f\left(x\right)=x^2-5x+6$

Part a) Step 2. Evaluate f(-2)

Substitute $-2$for $x$

$$\begin{gathered} f(-2)={(-2)}^2-5(-2)+6 \\ f(-2)=4+10+6 \\ f(-2)=20 \end{gathered}$$

Part b) Step 3. Evaluate f(3)

Substitute $3$for $x$

$$\begin{gathered} f\left(3\right)={\left(3\right)}^2-5\left(3\right)+6 \\ f\left(3\right)=9-15+6 \\ f\left(3\right)=-6+6 \\ f\left(3\right)=0 \end{gathered}$$

Part c) Step 4. Evaluate f(a)

Substitute $a$for $x$

$f\left(a\right)=a^2-5a+6$