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What is the domain of the function: #(2x-1) / (x²+2)#?

Answer 1

Eli Assouline

#D_f=R#

#x^2+2>0# for #AAx in R# so there aren't points of discontinuity and:

#D_f=R#

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Answer 2

Kennedy Adams

To find the domain of the function (\frac{2x - 1}{x^2 + 2}), we need to identify any values of (x) that would make the denominator equal to zero, as division by zero is undefined. Setting the denominator equal to zero and solving for (x), we get (x^2 + 2 = 0). However, this quadratic equation has no real solutions, as the square of any real number is always non-negative, and adding 2 to a non-negative number cannot result in zero. Therefore, there are no restrictions on the domain of the function. Hence, the domain of the function is all real numbers.

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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.