To evaluate [tex]\( f(3) \)[/tex] for the given function [tex]\( f(x) = \frac{12x^2 - 3x + 20}{3} \)[/tex], let's go through the process step-by-step.
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 inside the numerator:
[tex]\[
12(3)^2 - 3(3) + 20
\][/tex]
- First, calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
- Next, multiply by 12:
[tex]\[
12 \cdot 9 = 108
\][/tex]
- Then, multiply [tex]\( 3 \)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-3 \cdot 3 = -9
\][/tex]
- Finally, add 20:
[tex]\[
108 - 9 + 20 = 119
\][/tex]
So, the numerator becomes [tex]\( 119 \)[/tex].
3. Use the given denominator, which is 3:
[tex]\[
f(3) = \frac{119}{3}
\][/tex]
4. Simplify the fraction to obtain the decimal form:
[tex]\[
f(3) = 39.666666666666664
\][/tex]
Thus, the numerator is [tex]\( 119 \)[/tex], the denominator is [tex]\( 3 \)[/tex], and the simplified value of [tex]\( f(3) \)[/tex] is [tex]\( 39.666666666666664 \)[/tex].
So, in summary:
[tex]\[
f(3) = \frac{119}{3} = 39.666666666666664
\][/tex]
