Question

What is the domain of the function f(x)=sqrt(x^4-16)? In interval notation. Please show me how to work this problem out. I cannot find any examples in my book. Thanks!

Answer 1

You cannot take the square root of a negative. So f(x) is defined when the contents of the square root are greater than or equal to 0.

x^4 - 16 >= 0
x >= ? and x <= ?

Answer 2

Interval notation expresses an included endpoint (greater than or equal) with a "[]" and a not included endpoint (greater than) with a "()"

For example, if the domain of x is -2 < x <= 3, then interval notation would be (-2,3].