To find [tex]\( f(4) \)[/tex] for the function [tex]\( f(x) = x^2 - 3x + 7 \)[/tex], you need to substitute [tex]\( x = 4 \)[/tex] into the function and simplify.
Here's the detailed step-by-step solution:
1. Start with the given function:
[tex]\[
f(x) = x^2 - 3x + 7
\][/tex]
2. Substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[
f(4) = (4)^2 - 3(4) + 7
\][/tex]
3. Calculate the square of 4:
[tex]\[
(4)^2 = 16
\][/tex]
4. Multiply 3 by 4:
[tex]\[
3 \times 4 = 12
\][/tex]
5. Now substitute these values back into the expression:
[tex]\[
f(4) = 16 - 12 + 7
\][/tex]
6. Perform the subtraction and addition:
[tex]\[
16 - 12 = 4
\][/tex]
[tex]\[
4 + 7 = 11
\][/tex]
So, the value of [tex]\( f(4) \)[/tex] is [tex]\( 11 \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{11}
\][/tex]
