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Lunna [17]
3 years ago
13

Inverse Function In Exercise,analytically show that the functions are inverse functions.Then use the graphing utility to show th

is graphically.
f(x) = e^x - 1
g(x) = In(x + 1)

Mathematics
1 answer:
Anna [14]3 years ago
4 0

Step-by-step explanation:

We need to show whether

f^{-1}(x) = g(x)

or

g^{-1}(x) = f(x)

so we'll do either one of them,

we'll convert f(x) to f^-1(x) and lets see if it looks like g(x).

f(x) = e^x - 1

we can also write it as:

y = e^x - 1

now all we have to do is to make x the subject of the equation.

y+1 = e^x

\ln{(y+1)} = x

x=\ln{(y+1)}

now we'll interchange the variables

y=\ln{(x+1)}

this is the inverse of f(x)

f^{-1}(x)=\ln{(x+1)}

and it does equal to g(x)

g(x)=\ln{(x+1)}

Hence, both functions are inverse of each other!

This can be shown graphically too:

we can see that both functions are reflections of each other about the line y=x.

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Which property of real numbers IS shown below?<br> 3 + ((-5) + 6) = (3 + (-5)) + 6
Art [367]

The associative property of real numbers is shown in the number expression 3 + ((-5) + 6) = (3 + (-5)) + 6

<h3>What is an arithmetic operation?</h3>

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have a number expression:

= 3 + ((-5) + 6) = (3 + (-5)) + 6

As we know in the associative property:

a + (b + c) = (a + b) + c

= (3 + (-5)) + 6

Thus, the associative property of real numbers is shown in the number expression 3 + ((-5) + 6) = (3 + (-5)) + 6

Learn more about the arithmetic operation here:

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6 0
2 years ago
The sum of two consecutive integers is 345. What are the integers? need help with it
horrorfan [7]

Answer:

hi there ☺️

Here we will use algebra to find three consecutive integers whose sum is 345. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 345. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 345

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 345

3X + 3 = 345

3X + 3 - 3 = 345 - 3

3X = 342

3X/3 = 342/3

X = 114

Which means that the first number is 114, the second number is 114 + 1 and the third number is 114 + 2. Therefore, three consecutive integers that add up to 345 are 114, 115, and 116.

114 + 115 + 116 = 345

We know our answer is correct because 114 + 115 + 116 equals 345 as displayed above.

Step-by-step explanation:

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2 years ago
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Answer:

0.125 liters per day

Step-by-step explanation:

0.5/4=.125

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Answer:\

The answer to you is:

True

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Answer:

yes I can

Step-by-step explanation:

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