Question

the domain of the function f(x)= {(x²-9)÷(x-3),if x is not equal to 3
6, if x=2}​

Answer 1

The function $f(x)$ is defined as,

$\longrightarrow f(x)=\left\{\begin{array}{lc}\dfrac{x^2-9}{x-3},&x\neq3\\\\6,&x=3\end{array}\right.$

We're asked to find the domain of this function.

Since $f(x)=6$ at $x=3,$ the domain of the function includes the value 3.

Let,

$\longrightarrow y=\dfrac{x^2-9}{x-3}$

$\longrightarrow y=\dfrac{(x-3)(x+3)}{x-3}$

$\longrightarrow y=x+3$

The equation shows a straight line, so its domain would be the set of all real numbers.

$\longrightarrow x\in\mathbb{R}$

Hence the domain of the function is also $\mathbb{R}.$

$\longrightarrow x\in\mathbb{R}\cup\{3\}$

$\longrightarrow\underline{\underline{x\in\mathbb{R}}}$