Answer:
The domain is all real numbers but x ≠3
Step-by-step explanation:
f(x) = x+2
-------
x-3
The domain is all values except where the denominator is zero
x-3 ≠0
Add 3 to each side
x-3+3 ≠0+3
x ≠3
The domain is all real numbers but x ≠3
The domain of the function f(x) is:
We are given a function f(x) as follows:
[tex]f(x)=\dfrac{x+2}{x-3}[/tex]
We know that the domain of a function is the set of all the value of the independent variable i.e. x for which the function is well defined.
We know that the domain of the rational function is the set of all the real numbers excluding the x-values where the denominator is zero.
Here after looking at the function f(x) we observe that it is defined for all the real values except when x=3.
( since the denominator i.e. x-3 is equal to zero when x= 3)
