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How do you determine if #f(x)=(6x )/( x^2 + 6)# is an even or odd function?

Answer 1

Christian Antunez

Hence #f(-x)=-f(x)# the function is odd.

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Answer 2

Serenity Jones

To determine if a function is even or odd, we evaluate whether it satisfies the conditions of evenness or oddness:

Even function: f(x) = f(-x) for all x in the function's domain.
Odd function: f(x) = -f(-x) for all x in the function's domain.

For the function f(x) = (6x)/(x^2 + 6):

To check for evenness, substitute -x for x and see if the function remains the same. f(-x) = (6(-x))/((-x)^2 + 6) f(-x) = (-6x)/(x^2 + 6)
To check for oddness, substitute -x for x and see if the function becomes the negative of the original function. -f(-x) = -(6(-x))/((-x)^2 + 6) -f(-x) = (6x)/(x^2 + 6)

Comparing the results:

Since f(-x) = -f(x), the function is odd.

Therefore, f(x) = (6x)/(x^2 + 6) is an odd function.

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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.