Question

If $A=\{x:|x|\le 5;x\in Z-\{0\left\}\right\}$, $B=\{x:x\le 100;x\in W\}$ and $f:A\to B$ is a function defined by $f\left(x\right)=x^2+1$, then the number of elements in the range of $f$ that lie in $[5,26)$ is

• A. $5$
• B. $3$
• C. $4$
• D. $2$

Answer 1

The correct option is B $3$

$A=\{-5,-4,-3,-2,-1,1,2,3,4,5\}B=\{0,1,2,\cdots ,100\}$
$f\left(x\right)=x^2+1$
$f(-5)=f\left(5\right)=25+1=26f(-4)=f\left(4\right)=16+1=17f(-3)=f\left(3\right)=9+1=10f(-2)=f\left(2\right)=4+1=5f(-1)=f\left(1\right)=1+1=2$

$\therefore R\left(f\right)=\{2,5,10,17,26\}$
Hence, the required number of elements in $R\left(f\right)$ that lie in $[5,26)$ is $3$ i.e $\{5,10,17\}$