Sure, let's evaluate [tex]\( f(3) \)[/tex] for the given function [tex]\( f(x) = \frac{12x^2 - 3x + 20}{3} \)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \frac{12(3)^2 - 3(3) + 20}{3}
\][/tex]
2. Calculate the value of [tex]\( 12(3)^2 \)[/tex]:
[tex]\[
12 \cdot (3)^2 = 12 \cdot 9 = 108
\][/tex]
3. Calculate the value of [tex]\( -3(3) \)[/tex]:
[tex]\[
-3 \cdot 3 = -9
\][/tex]
4. Add these results along with 20:
[tex]\[
108 - 9 + 20 = 119
\][/tex]
5. Divide the sum by 3:
[tex]\[
f(3) = \frac{119}{3}
\][/tex]
So, the final result of evaluating [tex]\( f(3) \)[/tex] is:
[tex]\[
f(3) = 39.666666666666664
\][/tex]
Therefore, [tex]\( f(3) \)[/tex] evaluates to approximately [tex]\( 39.67 \)[/tex] when rounded to two decimal places.
