What is the domain of f(x)?

1/(sqrt(x-7)*(x^2-4)

1 Answer
Dec 31, 2017

x > 7 : x \in \RR

Explanation:

You have to avoid x values that makes the denominator zero.
So:
x^2-4 \ne 0
sqrt(x-7) > 0

Let's solve the first one:
x^2-4 = 0
x^2=4
x\ne\pm2

While the second one:
sqrt(x-7) > 0
x-7>0
x>7

The final results are x>7 and x\ne \pm2, but the first is stronger so the domain is:
x > 7 : x \in \RR

graph{1/(sqrt(x-7)*(x^2-4)) [4.32, 10.482, -0.642, 2.436]}