Question

If \(f: \mathbb{R} \rightarrow \mathbb{R}\) be defined by \(f(x) = \begin{cases}  2x & \text{if } x > 3 \\ x^2 & \text{if } 1 < x \leq 3 \\ 3x & \text{if } x \leq 1 \end{cases}\). Then \(f(-1) + f (2) + f(4)\) is

• A. 5
• B. 9
• C. 10
• D. 14

Answer 1

The Correct Option is B

First, let's calculate \(f(-1):\)
Since \(x ≤ 1\), we use the third part of the function definition:
\(f(-1) = 3(-1) = -3\)

Next, let's calculate \(f(2):\)
Since \(1 < x ≤ 3\), we use the second part of the function definition:
\(f(2) = (2)^2 = 4\)

Finally, let's calculate \(f(4):\)
Since \(x > 3\), we use the first part of the function definition:
\(f(4) = 2(4) = 8\)

Now, we can compute \(f(-1) + f(2) + f(4):\)
\(-3 + 4 + 8 = 9\)

Therefore, \(f(-1) + f(2) + f(4)\) is equal to 9 (option B).