Question

Evaluate f(x) when x = 10.

f(x) = 2x - 4 if 3 < x < 10
f(x) = x^2 + 3 if 10 ≤ x < 13


A) 16
B) 18
C) 22
D) 26

Answer 1

The correct evaluation of f(x) when x = 10, using the second function, results in f(x) = 103. This is not among the given options, indicating a potential mistake in the question's answer choices.

Step-by-step explanation:

To evaluate f(x) when x = 10, you need to determine which piece of the piecewise function applies for the value of x = 10. The given functions are f(x) = 2x - 4 if 3 < x < 10 and f(x) = x² + 3 if 10 ≤ x < 13. Since 10 is not greater than 10 but is equal to it, we use the second function, f(x) = x² + 3.

Substituting 10 into the second function, we get:
f(10) = 10² + 3 = 100 + 3 = 103

Therefore, the value of f(x) when x = 10 is 103, which is not one of the provided choices A) 16, B) 18, C) 22, or D) 26. It seems there might have been a mistake in the options given as none of them match the correct answer.