How do you find the domain of h(x)= sqrt( 4-x^2)/( x-3)?

1 Answer
Jun 11, 2015

The domain is restricted by the numerator to [-2, 2] and by the denominator to (-oo,3) uu (3,oo), which is no additional restriction. So the domain of h(x) is [-2, 2]

Explanation:

In order for the numerator of h(x) to be defined, 4 - x^2 >= 0.

Adding x^2 to both sides we get x^2 <= 4 = 2^2

hence -2 <= x <= 2

In order for the denominator to be defined and non-zero, we just need x != 3

This condition only affects values of x outside the [-2, 2] range we already know the domain is restricted to.

So h(x) is well defined for all x in [-2, 2].