How would you solve this?

Question

Find the domain of f. Enter your answer using interval notation.) f(x) = (x - 4)/(sqrt(x - 3))

Answer 1

Andrew's comment is spot on. For this case, here's the answer.

So, when we're asked for a domain, we're asked for acceptable inputs: values for x.

It's easier to find what's not acceptable: any x that would make us divide by zero or take the square root of a negative.

The denominator of this fraction is sqrt(x-3). That cannot equal zero, so what x would make it 0?

sqrt(x-3)=0

x-3=0

x=3 is an unacceptable domain value.

We also have a square root of something which cannot be negative, so what value(s) of x would make it negative?

x-3 < 0

x<3

So x cannot be 3 or less than 3.

So x must be greater than 3.

In interval notation: (3, +infinity)

Parentheses indicate unreachable values while brackets would indicate reachable values.