Let $A=\{-4,-2,-1,0,3,5\}$ and $f: \mathrm{A} \rightarrow \mathbf{R}$ be defined by…
Let $A=\{-4,-2,-1,0,3,5\}$ and $f: \mathrm{A} \rightarrow \mathbf{R}$ be defined by $f(x)=\left\{\begin{array}{ccc}3 x-1 & \text { for } & x>3 \\ x^2+1 & \text { for } & -3 \leq x \leq 3 \\ 2 x-3 & \text { for } & x < -3\end{array}\right.$ Then the range of $f$ is
$\{-11,5,2,1,10,14\}$
$\{-11,-7,2,1,8,14\}$
$\{-11,5,2,1,8,14\}$
$\{-11,-7,-5,1,10,14\}$
Solution
Here, function is defined for $f: A \rightarrow R$
$
f(x)=\left\{\begin{array}{ccc}
3 x-1 & \text { for } & x>3 \\
x^2+1 & \text { for } & -3 \leq x \leq 3 \\
2 x-3 & \text { for } & x < -3
\end{array}\right.
$
and $A=\{-4,-2,-1,0,3,5\}$
$
\begin{aligned}
& f(-4)=2(-4)-3=-11 \\
& f(-2)=(-2)^2+1=4+1=5
\end{aligned}
$
$
\begin{aligned}
& f(-1)=(-1)^2+1=1+1=2 \\
& f(0)=0^2+1=1 \\
& f(3)=3^2+1=10 \\
& f(5)=3(5)-1=14
\end{aligned}
$
Hence, range of $f$ is $\{-11,5,2,1,10,14\}$