Question

If $f:R-\left\{2\right\}\to R$ is a function defined by $f\left(x\right)=\frac{x^2-4}{x-2}$, then its range is

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

Answer 1

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

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

As the domain does not include $2$ we can simplyfy,

$f\left(x\right)=x+2$,

$\therefore$ $x$ can take any real value in the domain,

So,the range is $R-\left\{4\right\}$,

As is $x+2=4⟹x=2$ which is not in the domain.