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How do you find the domain in interval notation for #f(x)=x/(x^3+8) #?

Answer 1

Nathan Axel

#(x^3 + 8) = (x^3+2^3) = (x+2)(x^2-2x+4)#

has only one zero for real values of #x#, viz #x = -2#.

#f(x)# is well defined for all other values of #x#.

So the domain of #f(x)# is #(-oo, -2) uu (-2, oo)#

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Answer 2

Genesis Allen

To find the domain of the function ( f(x) = \frac{x}{x^3 + 8} ), we need to determine the values of ( x ) for which the function is defined. The function is undefined when the denominator ( x^3 + 8 ) equals zero, as division by zero is not defined. Thus, we need to find the values of ( x ) that make the denominator zero:

[ x^3 + 8 = 0 ]

By solving this equation, we find that ( x = -2 ) is the only real solution.

Therefore, the domain of the function in interval notation is:

[ \text{Domain: } (-\infty, -2) \cup (-2, \infty) ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.