Questions: Find the domain of the function f(x)=2/(x-3) x x ≠ 3 x x>3 x x<3

Transcript text: Find the domain of the function $f(x)=\frac{2}{x-3}$ $\{x \mid x \neq 3\}$ $\{x \mid x>3\}$ $\{x \mid x<3\}$

Solution

Solution Steps

Step 1: Identify the function

The given function is: \[ f(x) = \frac{2}{x - 3} \] This is a rational function, and its domain is all real numbers except where the denominator equals zero.

Step 2: Determine where the denominator is zero

Set the denominator equal to zero and solve for $ x $: \[ x - 3 = 0 \] \[ x = 3 \] The denominator is zero when $ x = 3 $, so $ x = 3 $ is excluded from the domain.

Step 3: Write the domain

The domain of $ f(x) $ is all real numbers except $ x = 3 $. In set notation, this is: \[ \{x \mid x \neq 3\} \]