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How do you find the domain in interval notation for #f(x)=(x+6)/(x^2+5) #?

Answer 1

The domain of a function is all the values that #x# can take (in order to avoid having something like #a/0#, which isn't defined).

In your case, #x^2+5 > 0# with #x in RR#; therefore, there is no way you could have a division by zero.

Thus, the domain #D = RR# or, in interval notation, #D = ]-oo;+oo[#.

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Answer 2

Hazel Anglin

To find the domain of the function ( f(x) = \frac{x + 6}{x^2 + 5} ) in interval notation, we need to identify any values of ( x ) that would make the denominator equal to zero. The denominator ( x^2 + 5 ) will be zero only if ( x^2 = -5 ). However, since there are no real numbers that satisfy this equation, the function has no restrictions on its domain. Therefore, the domain of ( f(x) ) in interval notation is ( (-\infty, \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.