Question

F(x)=1/2×+6 plz helpppppppppp​

Answer 1

The solution set can be given as:

`\x`

Explanation:

Given function:

`f(x)=(1)/(2x+6)`

To find the domain of the function in set notation.

Solution:

For the function
`f(x)` to exist the denominator must be ≠ 0

We have the denominator
`(2x+6)` which cannot be = 0.

Thus, we can find the domain of the function using the above relation.

The function
`f(x)` will not exist when:

`2x+6=0`

Solving for
`x`

Subtracting both sides by 6.

`2x+6-6=0-6`

`2x=-6`

Dividing both sides by 2.

`(2x)/(2)=(-6)/(2)`

∴
`x=-3`

Thus, the function will not exist at
`x=-3`. This means it has all real number solutions except -3.

The solution set can be given as:

`\x\ \epsilon\ R,x\\eq -3\`