Question

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

$f\left(x\right)=3x^2-2x+1$

Short answer

The function is $f\left(x\right)=3x^2-2x+1$

a) To evaluate $f(-2)$, so we get $9$

b) To evaluate $f\left(3\right)$, so we get $-1$

c) To evaluate$f\left(a\right)$, so we get$3a^2-2a+1$

Step-by-step solution

Part a) Step 1. Given Information

We have the function

$f\left(x\right)=3x^2-2x+1$

Part a) Step 2. Evaluate f(-2)

Substitute $-2$for $x$

$$\begin{gathered} f(-2)=3{(-2)}^2-2(-2)+1 \\ f(-2)=12+4+1 \\ f(-2)=17 \end{gathered}$$

Part b) Step 3. Evaluate f(3)

Susbtitute $3$for $x$

$$\begin{gathered} f\left(3\right)=3{\left(3\right)}^2-2\left(3\right)+1 \\ f\left(3\right)=27-6+1 \\ f\left(3\right)=22 \end{gathered}$$

Part c) Step 4. Evaluate f(a)

Substitute $a$for $x$

$$\begin{gathered} f\left(a\right)=3{\left(a\right)}^2-2\left(a\right)+1 \\ f\left(a\right)=3a^2-2a+1 \end{gathered}$$