Question

Mark the correct alternative in the following question:

Let f : R $\to$ R be defined as f(x) = $\left\{\begin{array}{c}2x,\mathrm{if}x>3\\ x^2,\mathrm{if}1<x\le 3\\ 3x,\mathrm{if}x\le 1\end{array}\right.$

Then, find f($-$1) + f(2) + f(4)

(a) 9 (b) 14 (c) 5 (d) none of these

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ f\left(x\right)=\left\{\begin{array}{c}2x,\mathrm{if}x>3\\ x^2,\mathrm{if}1<x\le 3\\ 3x,\mathrm{if}x\le 1\end{array}\right. \\ \mathrm{Now}, \\ f\left(-1\right)+f\left(2\right)+f\left(4\right) \\ =3\left(-1\right)+2^2+2\left(4\right) \\ =-3+4+8 \\ =9 \end{gathered}$$

Hence, the correct alternative is option (a).