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

Answer: (B)

9

Answer 2

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).