State the domain of the the function h(x) over f(x) using interval notation

Question

Given functions h(x) = 1 over sqrt(x) and f(x) = x^2 - 4, state the domain of the following using interval notation: h(x) over f(x)

Answer 1

Given: h(x) = 1/ sqrt(x) AND f(x) = x^2 - 4

Find: Domain of h(x) / f(x)

SOLUTION:

h(x) / f(x)

= [ 1 / sqrtIx) ] / [ x^2 - 4 ]

= 1 / [ sqrt(x) * (x^2 - 4) ]

The term sqrt(x) is used so x >= 0

Also, the term sqrt(x) is in the denominator

So, x > 0 Because Denom. cannot be zero.

The term (x^2 - 4) is also in the denominator

Therefore, x cannot be +/- 2. Denom. cannot be zero.

(-infinity, -2) U (-2, 2) U (2, infinity)

But, x > 0 Note: x cannot be negative.

So, the DOMAIN, in interval notation, is:

(0, 2) U (2, infinity)