Certainly! Let's evaluate [tex]\( f(3) \)[/tex] given the function [tex]\( f(x) \)[/tex].
The given function is:
[tex]\[ f(x) = \frac{12x^2 - 3x + 20}{3} \][/tex]
To find [tex]\( f(3) \)[/tex], we need to substitute [tex]\( x = 3 \)[/tex] into the function:
1. Start with the expression inside the function:
[tex]\[ 12x^2 - 3x + 20 \][/tex]
Substituting [tex]\( x = 3 \)[/tex]:
[tex]\[ 12(3)^2 - 3(3) + 20 \][/tex]
2. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]
3. Substitute [tex]\( 9 \)[/tex] into the expression:
[tex]\[ 12 \times 9 - 3 \times 3 + 20 \][/tex]
4. Perform the multiplications:
[tex]\[ 12 \times 9 = 108 \][/tex]
[tex]\[ 3 \times 3 = 9 \][/tex]
5. Substitute these values back into the expression:
[tex]\[ 108 - 9 + 20 \][/tex]
6. Perform the addition and subtraction:
[tex]\[ 108 - 9 = 99 \][/tex]
[tex]\[ 99 + 20 = 119 \][/tex]
So, the expression inside the function, when [tex]\( x = 3 \)[/tex], is 119.
Now the function [tex]\( f(x) \)[/tex] is:
[tex]\[ f(x) = \frac{12x^2 - 3x + 20}{3} \][/tex]
Substitute the value we obtained:
[tex]\[ f(3) = \frac{119}{3} \][/tex]
Finally, simplify the division:
[tex]\[ \frac{119}{3} = 39.666666666666664 \][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is:
[tex]\[ f(3) = 39.666666666666664 \][/tex]
