Question

Find the range of the function $f\left(x\right)=\frac{x^2-4}{x-2}$ for $x\ne 2$ .

• A. $R$
• B. $R-\left\{0\right\}$
• C. $R-\left\{2\right\}$
• D. $R-\left\{4\right\}$

Answer 1

The correct option is D $R-\left\{4\right\}$

Given, $f\left(x\right)=\frac{x^2-4}{x-2}$ for $x\ne 2$

Therefore, $f\left(x\right)=\frac{(x+2)(x-2)}{x-2}=x+2$ for $x\ne 2$
When $x\ne 2$, $f\left(2\right)=4$ not possible.
$\therefore$ Range is $R-\left\{4\right\}$