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

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

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

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

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