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How do you find the domain in interval notation for #f(x)=sqrt(x+7)/(x^2+7)#?

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Jun 2, 2015

First note that for all #x in RR#, #x^2+7 >= 7#, so the denominator will always be non-zero.

Next note that #sqrt(x+7)# is defined when #x+7 >= 0#, that is when #x >= -7#.

So #f(x)# is well defined for #x in [-7, oo)# which is therefore the domain of #f(x)#.

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