Question

Identify the restrictions on the domain of f(x) = quantity x plus 2 over quantity x minus 3

Answer 1

The domain of the function f(x) is:

• All the real values except x=3

Explanation:

We are given a function f(x) as follows:

`f(x)=(x+2)/(x-3)`

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)

Answer 2

The domain is all real numbers but x ≠3

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