Question

The range of the function $f\left(x\right)=\frac{x^2+2x+1}{x^2-8x+12}$ is

• A. R\$\{1,-\frac{1}{2}\}$
• B. $R-(2,6)$
• C. R\ $\left\{1\right\}$
• D. $noneofthese$

Answer 1

The correct option is B $R-(2,6)$

We have,

$\frac{x^2+2x+1}{x^2-8x+12}$

$=\frac{(x+1{)}^2}{x^2-2x-6x+12}$

$=\frac{(x+1{)}^2}{x(x-2)-6(x-2)}$

$=\frac{(x+1{)}^2}{(x-2)(x-6)}$

The denominator cannot be zero. Hence, $(x-6)(x-2)\ne 0$.

$\Rightarrow x\ne 6$ and $x\ne 2$

$\therefore$ The Domain $=R-\{2,6\}$

Hence, this is answer.