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Single Variable Calculus

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Moderate

A Log, a Composition, and a Tricky Domain

SVCALC-VA1KEL

Given the functions

$$g(x)\quad =\quad 4-{ x }^{ 2 }$$

$$f(x)\quad =\quad \ln{ x } $$

Find the domain of

$$(f\circ g)(x)$$

A

$(0,\infty )$

B

$(2,\infty )$

C

$(-2,2)$

D

$(-\infty ,-2)$

E

$(-\infty ,-2)\cup (2,\infty )$