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).

Answer 2

We are given a piecewise function: \[ f(x) = \begin{cases} 2x & \text{if } x > 3 \\ x^2 & \text{if } 1 < x \leq 3 \\ 3x & \text{if } x \leq 1 \end{cases} \] We need to find: \[ f(-1) + f(2) + f(4) \]

Step 1: Evaluate f(-1)
Since -1 ≤ 1, we use: f(x) = 3x
So, f(-1) = 3 × (-1) = -3

Step 2: Evaluate f(2)
Since 1 < 2 ≤ 3, we use: f(x) = x²
So, f(2) = 2² = 4

Step 3: Evaluate f(4)
Since 4 > 3, we use: f(x) = 2x
So, f(4) = 2 × 4 = 8

Final Step:
\[ f(-1) + f(2) + f(4) = -3 + 4 + 8 = 9 \]
 Answer: 9

Answer 3

We are given the function:

\(f(x) = \begin{cases} 2x & \text{if } x > 3 \\ x^2 & \text{if } 1 < x \leq 3 \\ 3x & \text{if } x \leq 1 \end{cases}\)

We need to find \(f(-1) + f(2) + f(4)\).

1. f(-1): Since -1 ≤ 1, we use the third case: f(x) = 3x

f(-1) = 3(-1) = -3

2. f(2): Since 1 < 2 ≤ 3, we use the second case: f(x) = x²

f(2) = (2)² = 4

3. f(4): Since 4 > 3, we use the first case: f(x) = 2x

f(4) = 2(4) = 8

Now, we add the values:

f(-1) + f(2) + f(4) = -3 + 4 + 8 = 9

Answer: 9