Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Exercise Set - Page 258: 19

$(3, +\infty)$

Work Step by Step

The denominator is not allowed to be zero as division of zero leads to an undefined expression. This means that $x$ cannot be equal to $3$. The radicand (expression inside a radical) of a square root cannot be negative as its root is an imaginary number. Thus, the value of $x$ can be any real number that is greater than or equal to $3$. The restrictions to the value of $x$ are: (1) $x \ne 3$; (2) $x \ge 3$ This means that the value of $x$ has to be greater than $3$. Therefore, the domain of the given function is $(3, +\infty)$.

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