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Orlov [11]
3 years ago
6

What is the inverse of the function f(x) = 2x + 1?

Mathematics
2 answers:
Marina CMI [18]3 years ago
5 0

Answer:

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

Step-by-step explanation:

f(x) = 2x + 1

f(x) = y (output)

y = 2x + 1

Solve for x.

y - 1 = 2x

Divide 2 on both sides.

y/2 - 1/2 = x

1/2y - 1/2 = x

Switch variables.

1/2x - 1/2 = y

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

BaLLatris [955]3 years ago
3 0

Answer:

f^{-1} = \frac{x-1}{2}

Step-by-step explanation:

f(x) = 2x+1

<em>Replace it with y</em>

y = 2x+1

<em>Exchange the values of  x and y</em>

x = 2y+1

<em>Solve for y</em>

x = 2y+1

<em>Subtracting 1 from both sides</em>

2y = x-1

<em>Dividing both sides by 2</em>

y = \frac{x-1}{2}

<em>Replace it by </em>f^{-1}

So,

f^{-1} = \frac{x-1}{2}

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Answer:

<u></u>

  • <u>Part A: No, you cannot.</u>

<u></u>

  • <u>Part B: 0.4491</u>

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<u>Part A:</u>

The mean of samples of symmetrical (bell shaped) distributions follow a normal distribution pattern.

Thus, for symmetrical distributions you can use the z-score tables to make calculations that permit calculate probabilities for particular values.

For <em>skewed </em>distributions, in general, the samples do not follow a normal distribution pattern, except that the samples are large.

Since <em>a sample of 20 pictures</em> is not large enough, the answer to this question is negative: <em>you cannot accurately calculate the probability that the mean picture size is more than 3.8MB for an SRS (skewed right sample) of 20 pictures.</em>

<u>Part B.</u>

For large samples, the<em> Central Limit Theorem</em> will let you work with samples from skewed distributions.

Although the distribution of a population is skewed, the <em>Central Limit Theorem</em> states that  large samples follow a normal distribution shape.

It is accepted that samples of 30 data is large enough to use the <em>Central Limit Theorem.</em>

Hence, you can use the z-core tables for standard normal distributions to calculate the probabilities for a <em>random sample of 60 pictures</em> instead of 20.

The z-score is calculated with the formula:

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Here, mean = 3.7MB, value = 3.8MB, and standard deviation = 0.78MB.

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         z=(3.7M-3.8MB)/(0.78MB)=-0.128

Then, you must use the z-score table to find the probability that the z-score is greater than - 0.128.

There are tables that show the cumulative probability in the right end and tables that show the cumulative probability in the left end of a normal standard distribution .

The probability that a z-score is greater than -0.128 is taken directly from a table with the cumulative probability in the left end. It is 0.4491.

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