Use interval notation to indicate the domain of each radical function

Question

Use interval notation to indicate the domain of each radical function

g(x)=^5√8+x The formula is the sqrt of 8+x to the fifth power.

Answer 1

g(x) = (√ (8+x))⁵

The domain is all x values for which we can evaluate g(x)

As g(x) has a square root, the radicand (expression under the square root) must be >= 0

[ using real numbers we cannot evaluate the square root of a negative number ]

so 8+ x > = 0, so x >= -8

So domain is [-8, +∞)