Question

What is the value of f(–10.1) for the function f(x)={S-|2x - 9| if x < -4, 3.5x³ if x > -4?

A) 35.735
B) 37.15
C) 371.5
D) 375.3

Answer 1

The value of f(–10.1) for the function is -29.2, using the definition for x < -4. However, this value is not in the provided multiple-choice options, which suggests there might be an error in the question.

Step-by-step explanation:

The student is asking for the value of f(–10.1) given a piecewise function where f(x) = -|2x - 9| if x < -4, and f(x) = 3.5x³ if x > -4. Since -10.1 < -4, we use the first part of the function to evaluate f(–10.1).

First calculate 2x - 9 with x = -10.1:

2(-10.1) - 9 = -20.2 - 9 = -29.2

Then, we take the absolute value of -29.2, which is 29.2, and finally apply the negative sign as per the function definition:

-|2(-10.1) - 9| = -29.2

Therefore, the value of f(–10.1) is -29.2, which is not included in the given options A) 35.735 B) 37.15 C) 371.5 D) 375.3. The question might contain an error as the calculated value does not match any of the choices provided.