Question

Consider the following function: f(x) = 5x - 10 cos(x), -2 ≤ x ≤ 0. What is the value of f(-2)?

1) 0
2) 10
3) 20
4) 30

Answer 1

When computing the value of f(-2) for the function f(x) = 5x - 10 cos(x), the result is approximately -5.8385, which is not among the provided answer choices.

Step-by-step explanation:

To find the value of the function f(x) = 5x - 10 cos(x) at x = -2, we simply plug in the value of x into the function:

• f(-2) = 5(-2) - 10 cos(-2)
• f(-2) = -10 - 10 cos(-2)

Since the cosine function is even, cos(-θ) = cos(θ), therefore:

• f(-2) = -10 - 10 cos(2)

Next, we need to calculate the value of cos(2). Cosine of 2, which is approximately cos(2) ≈ -0.41615 (using a calculator), therefore:

• f(-2) = -10 - 10(-0.41615)
• f(-2) = -10 + 4.1615
• f(-2) = -5.8385

However, the possible answers given are all positive and do not include the calculated value. It is possible that there is a mistake in the question or the answer choices. We do not have the exact value of -5.8385 as an option. In assuming that it may be a typo or the answers provided are mistaken, based on the calculations f(-2) is neither 0, 10, 20, or 30.