Question

What is the domain of the relation {(x,y):Y= x(x-3)/ (X+4) (X-7)

Answer 1

The domain is the x of a relation, whereas the range is the y.

Answer 2

The domain is:

x ∈ R / {x ≠ -4, 7}

All the real numbers except -4 and 7

How to get the domain?

Here we have the relation:

y = x*(x - 3)/(x + 4)*(x - 7)

Remember that we start assuming the domain is the set of all real numbers, then we remove the problematic ones.

Here the problematic ones are these values of x that make the denominator equal to zero.

The denominator is (x + 4)*(x - 7)

x = -4 and x = 7 make this denominator zero, so we need to remove these values from the domain.

The domain is:

x ∈ R / {x = -4, 7}