The domain of the function in the correct set notation is {x|x∈R x≠-3}.
The domain of a function is the set of all possible inputs that the function can have.
The function is given to be f(x)=1 /(2x+6).
Here, we can see that the function would become not be defined if the denominator becomes zero.
Therefore, the domain should not contain the values which make it not defined.
The value of x for which it becomes zero can be determined below:
2x+6=0
2x=-6
x=-3
Therefore, the domain must contain all values of real numbers except -3.
The domain of the function is found. The domain of the function is the set of all real numbers except -3. It can be written as {x|x∈R x≠-3}.
Therefore, we have found the domain of the function in the correct set notation is {x|x∈R x≠-3}.
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