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2 years ago

Which represents the inverse of the function f(x) = 4x?

Mathematics

1 answer:

Viktor [21]2 years ago

6 0

Answer:

last answer:

h(x) = 1/4 x

Step-by-step explanation:

First, change f(x) to y.

f(x) = 4x

y = 4x

Then switch the x and y.

y = 4x

x = 4y

Last, solve for y.

x = 4y

x/4 = 4y/4

x/4 = y

y = x/4

This is the same as:

y = 1/4 x

h(x) = 1/4 x

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Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 $s = \frac{\sigma}{\sqrt{n}}$ .