Question

F(x)=1/2×+6 plz helpppppppppp​

Answer 1

Answer:

The solution set can be given as:

$\{x|x\ \epsilon\ R,x\neq -3\}$

Step-by-step explanation:

Given function:

$f(x)=\frac{1}{2x+6}$

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.

$\frac{2x}{2}=\frac{-6}{2}$

∴ $x=-3$

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:

$\{x|x\ \epsilon\ R,x\neq -3\}$