Question

Let $f:R\to R$ be defined by

$f\left(x\right)=\{\begin{array}{ccc}2x,x>3& & \\ x^2,1<x\le 3& & \\ 3x,x\le 1& & \end{array}$

Then $f(-1)+f\left(2\right)+f\left(4\right)$ is

• A. $9$
• B. $14$
• C. None of these
• D. $5$

Answer 1

The correct option is A $9$

Find the value of given function for a particular value of $x$ on the defintion.

$f\left(x\right)=3xforx\le 1$

$\Rightarrow f(-1)=3(-1)=-3$

$\&f\left(x\right)=x^{2}for1<x\le 3$

$\Rightarrow f\left(2\right)=2^2=4$

$\&f\left(x\right)=2xforx>3$

$\Rightarrow f\left(4\right)=2\left(4\right)=8$

Then $f(-1)+f\left(2\right)+f\left(4\right)=-3+4+8=9$

Hence, option (a) is correct.