Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = 5x^2 - 9x + 18 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = 5(3)^2 - 9(3) + 18
\][/tex]
2. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
3. Multiply the result by 5:
[tex]\[
5 \times 9 = 45
\][/tex]
4. Multiply 9 by 3:
[tex]\[
9 \times 3 = 27
\][/tex]
5. Substitute these values back into the equation:
[tex]\[
f(3) = 45 - 27 + 18
\][/tex]
6. Perform the subtraction:
[tex]\[
45 - 27 = 18
\][/tex]
7. Add the remaining value:
[tex]\[
18 + 18 = 36
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is 36. Therefore, the correct answer is [tex]\( \boxed{36} \)[/tex], which corresponds to option B.
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = 5(3)^2 - 9(3) + 18
\][/tex]
2. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
3. Multiply the result by 5:
[tex]\[
5 \times 9 = 45
\][/tex]
4. Multiply 9 by 3:
[tex]\[
9 \times 3 = 27
\][/tex]
5. Substitute these values back into the equation:
[tex]\[
f(3) = 45 - 27 + 18
\][/tex]
6. Perform the subtraction:
[tex]\[
45 - 27 = 18
\][/tex]
7. Add the remaining value:
[tex]\[
18 + 18 = 36
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is 36. Therefore, the correct answer is [tex]\( \boxed{36} \)[/tex], which corresponds to option B.
