Question 389690
a){{{f(x) = sqrt((x - 3)/(2x^2 - 8))}}}
{{{f(x) = sqrt(x - 3)/sqrt(2x^2 - 8))}}}
if {{{x = 3}}}
The numerator is {{{0}}} and the denominator is (+)
and
If {{{x < 3}}}, The numerator is imaginary
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If {{{x > 3}}}, numerator is (+)
and denominator is (+)
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If {{{x = 2}}}
The denominator is {{{0}}}
and the numerator is imaginary
If {{{x < 2}}}, the denominator is imaginary
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The restriction {{{x > = 3}}} includes 
the restriction {{{x > 2}}}, so that is the domain
{{{x >= 3}}} answer

b) {{{f(x) = root(3,(x + 5)/(x^2 - 9))}}}.
{{{f(x) = root(3,(x + 5))/root(3,(x^2 - 9))}}}
If {{{x = -5}}} the numerator is {{{0}}} 
and the denominator is (+)
If {{{x < -5}}} the numerator is (-) 
and the denominator is (+) 
If {{{x > -5}}} the numerator is (-) 
and the denominator is (+) or (-)
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If {{{x = 3}}}, the denominator is {{{0}}}
If {{{x < 3}}} or {{{x > 3}}} denominator is (+)
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{{{x = 3}}} not allowed is the only restriction
The domain is {{{x > 3}}} and {{{x < 3}}}