Question
Find the domain and range of the real function \[f(x)=\frac{x^2-9}{x-3}\]
✓
Answer
Given, $f(x)=\frac{x^2-9}{x-3}$
Domain : Clearly, $f(x)$ is defined for all $x \in R$ except $x=3$
$\therefore$ Domain of $f=R-\{3\}$
Range : Let $y=f(x)$
$\therefore \quad y=\frac{x^2-9}{x-3} \Rightarrow y=x+3$
It follows from the above relation that $y$ takes all real values except 6 when $x$ takes values in the set $R-\{3\}$.
$\therefore \quad$ Range of $f=R-\{6\}$
Domain : Clearly, $f(x)$ is defined for all $x \in R$ except $x=3$
$\therefore$ Domain of $f=R-\{3\}$
Range : Let $y=f(x)$
$\therefore \quad y=\frac{x^2-9}{x-3} \Rightarrow y=x+3$
It follows from the above relation that $y$ takes all real values except 6 when $x$ takes values in the set $R-\{3\}$.
$\therefore \quad$ Range of $f=R-\{6\}$
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