What's the definition amount of : f(x) #sqrt(x+2)/x^3# ?

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#sqrt(x+2)/x^3#

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Answer 1 · 2018-02-28T19:59:40

#D_f = [-2, 0)∪(0,∞)#

The (natural) domain of a function is the largest set upon which its outputs are defined.

In this case, #f(x)=sqrt(x+2)/x^3#

The numerator is radical, so must always be non-negative

#x+2≥0 rArr x≥-2#

The denominator must not be zero, so #x≠0#.

Putting these two together, we get the domain as

#D_f=[-2, 0)∪(0,∞)#