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1-141.

Find the domain for each of the following functions. Note: The functions mentioned in parts (c) and (d) refer to those in parts (a) and (b).

1. $f ( x ) = \frac { 1 } { x + 2 }$

Visualize $f(x)$. It is a horizontal shift of $y=\frac{1}{x}$, which has a vertical asymptote at $x = 0$$f(x)$ also has a vertical asymptote. Where is it, and how will the vertical asymptote restrict the domain?

1. $g ( x ) = \sqrt { x - 4 }$

Visualize $g(x)$. It is a horizontal shift of
$y=\sqrt{x}$, which does not exist for negative values of $x$. What can you conclude about $g(x)$?

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

Find the domain of $\left ( \frac{1}{\sqrt{x-4}+2} \right )$

Both the square root and the denominator have restricted domains. Combine.

1. $k ( x ) = g ( f ( x ) )$

Refer to hints in part (c).