Question

Find the domain of the rational function below.

f(x)=(x+2)(x-1)/(x-3)(x+2)

Answer 1

Domain: x ≠ -2, 3

Explanation:

`f(x)=((x+2)(x-1))/((x-3)(x+2))`

The domain (x-values) of a rational function is all real numbers of x with the exception of those for which the denominator is 0. Therefore, to find the values of x that need to be excluded from the domain, equate the denominator to zero and solve for x.

The denominator for the given function is
`(x - 3)(x + 2)`

`\implies (x - 3)(x + 2)=0`

`\implies (x - 3)=0\implies x=3`

`\implies (x + 2)=0 \implies x=-2`

There will be a hole at x = -2 and an asymptote at x = 3.

So the values of x that need to be excluded from the domain are:

x = 3 and x = -2

Therefore, the domain of the given rational function is: x ∈ R