To evaluate [tex]\( f(3) \)[/tex] given the function [tex]\( f(x) = \frac{12x^2 - 3x + 20}{3} \)[/tex], follow these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \frac{12(3)^2 - 3(3) + 20}{3}
\][/tex]
2. Calculate the expression in the numerator:
- Compute [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
- Multiply by 12:
[tex]\[
12 \times 9 = 108
\][/tex]
- Multiply [tex]\( -3 \)[/tex] by 3:
[tex]\[
-3 \times 3 = -9
\][/tex]
- Add the constant term 20:
[tex]\[
108 - 9 + 20 = 119
\][/tex]
Therefore, the numerator is 119.
3. Divide the numerator by 3:
[tex]\[
f(3) = \frac{119}{3}
\][/tex]
4. Simplify the fraction:
The simplified fraction is:
[tex]\[
f(3) = 39.666666666666664
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 39.666666666666664 \)[/tex].
