Science:Math Exam Resources/Courses/MATH110/December 2013/Question 04 (b)/Solution 1

Looking at the outside function, we want to find $\sqrt{x}-1\ge 0$ for $\sqrt{\sqrt{x}-1}$ to be defined.

So we want $\sqrt{x}\ge 1$. Looking at the inside function, we want $\sqrt{x}\ge 0$ so $x\ge 0$.

Combining the two, we get:$x\ge 0$ and $x\ge 1$.

Hence the domain of $g(x)$ is $\{x\mathbb{ℝ}\mid x\ge 1\}$ or $x\in [1,\mathrm{\infty })$.