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3 years ago

Determine whether the ffunction X/(x^2-1) is odd even or neither

Mathematics

1 answer:

djyliett [7]3 years ago

3 0

equation is:

$f(x) = \frac{x}{ {x}^{2} - 1 }$

so if its even f(-x) should be equal to f(x)

that means

$f( - x) = \frac{ - x}{ {( - x)}^{2} - 1} \\ \\ f( - x) = - \frac{ x}{ {x}^{2} - 1}$

so f(x) is not equal to f(-x) so its not even

If its odd than f(-x) should be equal to -f(x)

$- f(x) = - ( \frac{ x}{ { x}^{2} - 1 } ) \\ - f(x) = - \frac{ x}{ {x}^{2} - 1 }$

so as we can see f(-x)= - f(x)

so the function is odd

Ans:function is odd and not even

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Answer:

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To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

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$Z = \frac{X - \mu}{\sigma}$

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Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 591, \sigma = 42$

What is the probability that a randomly selected application will report a GMAT score of less than 600?

This is the pvalue of Z when X = 600. So

$Z = \frac{X - \mu}{\sigma}$

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$Z = \frac{600 - 591}{5.94}$

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