Question

Range of the function $f\left(x\right)=\left(\frac{x^2-9}{x-3}\right)$ is

• A. $R$
• B. $R-\left\{3\right\}$
• C. $\left\{1\right\}$
• D. $R-\left\{6\right\}$

Answer 1

The correct option is D $R-\left\{6\right\}$

Given $f\left(x\right)=\frac{x^2-9}{x-3}$

$=\frac{(x-3)(x+3)}{(x-3)}$

$=x+3$ $[\because x\ne 3]$

So, at x=3, y=6 which will excluded in range Hence range $=R-\left\{6\right\}$