# Let $f:R \rightarrow R$ be defined by $f(x)=\left \{ \begin{array}{1 1} 2x:x>3\\x^2:1<1x\leq 3\\ 3x:x\leq1\end{array} \right.$ $Then\;f(-1)+f(2)+f(4)\;is$

\begin{array}{1 1}(A)\;9 & (B)\;14\\(C)\;5 & (D)\;none\;of\;these\end{array}

Toolbox:
• For the given function
• $f(x)= \left\{ \begin{array}{1 1} 2x & \quad ;x > 3 \\ x^2 & \quad ;1 < x \leq 3 \\3x & \quad ;x \leq 1 \end{array} \right.$
• for $f(-1) \qquad f(x)=3x \qquad -1 \leq 1$
• for $f(2) \qquad f(x)=x^2 \qquad 1 < 2 \leq 3$
• for $f(4) \qquad f(x)=2x \qquad x > 3$
$f(x)= \left\{ \begin{array}{1 1} 2x & \quad ;x > 3 \\ x^2 & \quad ;1 < x \leq 3 \\3x & \quad ;x \leq 1 \end{array} \right.$

$f(-1)+f(2)+f(4)$

$=3(-1)+2^2+ 2 \times 4$

$=-3+4+8$

$=9$

'A' option is correct