Question

If A={1,2,3,4} and $f:A\to R$ is a function defined by $f\left(x\right)=\frac{x^2-x+1}{x+1}$ then find the range of 'f'

Answer 1

Given $A=\{1,2,3,4\}$

$f:A\to R$ such that $f\left(x\right)=\frac{x^2-x+1}{x+1}$

$f\left(1\right)=\frac{1^2-1+1}{1+1}=\frac{1}{2}$

$f\left(2\right)=\frac{2^2-2+1}{2+1}=\frac{4-2+1}{3}=\frac{3}{3}=1$

$f\left(3\right)=\frac{3^2-3+1}{3+1}=\frac{9-3+1}{4}=\frac{7}{4}$

$f\left(4\right)=\frac{4^2-4+1}{4+1}=\frac{16-4+1}{5}=\frac{13}{5}$

$\therefore$ Range of $f=\{\frac{1}{2},1,\frac{7}{4},\frac{13}{5}\}$