### Home > CALC > Chapter 4 > Lesson 4.4.2 > Problem4-139

4-139.

For $f(x) =\operatorname{sin}(x^2)$, $g ( x ) = \sqrt { x - 2 }$, and $h ( x ) = \frac { 1 } { x }$, find the following functions and their domains.

1. $f(g(x))$

1. $f(g(h(x)))$

Careful: $f(g(h(x)))$ has a restricted domain.

1. $h(f(g(x)))$

$h(\text{part (a)})=\frac{1}{\text{(part (a))}}=$

Domain: Denominator cannot equal zero. For what value(s) of $x$ does $\operatorname{sin}(x-2) = 0$? Also, due to the square root in the original function, $x-2 ≥ 0$.

Domain: $x > 2$ and $x ≠ 2+$,$πn$, where $n$ is an integer value.

1. $h(h(x))$

$h(h(x))=\frac{1}{\frac{1}{x}}$
Simplify!