Answer:
The solution set can be given as:
[tex]\{x|x\ \epsilon\ R,x\neq -3\}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\frac{1}{2x+6}[/tex]
To find the domain of the function in set notation.
Solution:
For the function [tex]f(x)[/tex] to exist the denominator must be ≠ 0
We have the denominator [tex](2x+6)[/tex] which cannot be = 0.
Thus, we can find the domain of the function using the above relation.
The function [tex]f(x)[/tex] will not exist when:
[tex]2x+6=0[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 6.
[tex]2x+6-6=0-6[/tex]
[tex]2x=-6[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}=\frac{-6}{2}[/tex]
∴ [tex]x=-3[/tex]
Thus, the function will not exist at [tex]x=-3[/tex]. This means it has all real number solutions except -3.
The solution set can be given as:
[tex]\{x|x\ \epsilon\ R,x\neq -3\}[/tex]
