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azamat
2 years ago
10

Are exponential function one to one. How can you tell? What does this tell you about their inverses

Mathematics
1 answer:
aleksandrvk [35]2 years ago
5 0

See in the explanation

<h2>Explanation:</h2>

<h3>1. Are exponential function one to one. How can you tell?</h3>
  • A function f is one-to-one if each value of x corresponds to exactly one value of y.

To demonstrate this, we take the Horizontal Line Test that states:

<em>A function f has an inverse function if and only if there is no any horizontal line that intersects the graph of f at more than one point.</em>

As you can see in the first figure, the horizontal line y=3 (the green one) intersects the graph of the exponential function y=e^x (the red one) in just one point. If you take every horizontal line y=y_{0} with y_{0} any real number, you will find that every line intersects the exponential function in just one point. Therefore, this function is one-to-one

<h3>2. What does this tell you about their inverses?</h3>

Another important thing is that:

  • A function has an inverse function if and only if is one-to-one.  

As we have demonstrated that exponential functions are one-to-one by Horizontal Line Test, then we conclude exponential functions have inverse functions. The domain of the inverse function is the range of the original one and the range of the inverse function is the domain of the original one. The inverse of y=e^x is y=ln(x) whose graph is the second figure below.

<h2>Learn more: </h2>

How to find the inverse of a function? brainly.com/question/9980183

#LearnWithBrainly

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Research indicates that the leading brand of laundry detergent accounted for 35% of the 400,000 total sales in the marketplace.
Lesechka [4]

Answer:

140,000

Step-by-step explanation:

Take 400,000 * 0.35 = 140,000.

When given a percentage, take the number and divide by 100.

In this case 35 / 100 = 0.35.

Then you can take the total amount and multiply it by the percentage in decimal form.

In this case 400,000 * 0.35

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2 years ago
Mentally confused, please help.
garik1379 [7]
If you are looking for the surface area of the cube, it is 169. The equation for the surface area of a square is base times height. This would mean it’s 13x13 since all the sides are the same. 13x13=169
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2 years ago
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3 years ago
Some of the students three scores is 231. If the first is 20 points more than the second, and the sum of the first two is 6 more
Aleks [24]

Answer:

The first score is 109

Step-by-step explanation:

I am assuming that in the first sentence of the question, you meant:

Sum of the students three scores is 231...

First, let the scores of the first second and third student be a, b and c respectively. We are told that:

a + b + c = 231 . . . . . . . .(1)         (sum of students three scores is 231)

a = b + 20 . . . . . . . . . . . (2)        (the first is 20 points more than the second)

a + b = 6c . . . . . . . . . . . .(3)        (sum of the first two is 6 more times the third)

required, find a.

substituting the value of (a + b) in equation (3) into equation (1), we will have the following:

since a + b = 6c . . . (3)

a + b + c = 231 . . . . . (1), becomes,

(a + b) + c = 231

(6c)  + c = 231

7c = 231 (divide both sides by 7)

c = 231 ÷ 7 = 33

∴ c = 33

Next, from equation (2), we know that a = b + 20; this can also be written as:

a - 20 = b

∴ b = a - 20 . . . . . . . (4)

Finally, putting the value of b in equation (4) and the value of c calculated above into equation 1, ( a + b + c = 231), we have the following:

a + (a - 20) + 33 = 231

(a + a) - 20 + 33 = 231

2a + 13 = 231

2a = 231 - 13 = 218

a = 218 ÷ 2 = 109

∴ a = 109

we can also calculate for 'b' by substituting for the value of 'a' in equation 4

b = a - 20 = 109 - 20 = 89.

and to test if the values of a, b and c are correct:

a + b + c = 231

109 + 89 + 33 = 231

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3 years ago
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