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Ierofanga [76]
3 years ago
7

Let f(x)=e^x+3 show that f^-1(x)=ln x-3 can someone explain this to me

Mathematics
1 answer:
andrey2020 [161]3 years ago
3 0

Explanation:

For a function ...

  y = f(x)

the inverse function is ...

  x = f(y)

To write that in the form y=f^-1(x), you need to solve for y.

__

For your function f(x) = e^x +3 this looks like ...

  x = e^y +3

  x -3 = e^y . . . . . subtract 3

  ln(x -3) = y . . . . . take the natural log

So, we can write ...

  f^-1(x) = ln(x -3)

_____

Attached is a graph of these functions. As you might guess from the interchange of x and y, a function and its inverse are mirror images of each other across the line y=x.

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1/(x+1) + 1/a(x+1) find the lcm​
azamat

Answer:

See below.

Step-by-step explanation:

1/(x + 1) consists of 1 factor, 1/(x + 1)

1/[a(x + 1)] consists of two factors, 1/a and 1/(x + 1)

The LCM is 1/[a(x + 1)]

The LCD is a(x + 1)

5 0
3 years ago
Plzz anyone solve all answers plzzzzzzzz​
algol13

You posted a lot of problems here. In the future please only post one problem at a time. Thank you.

I'll do the first two problems to get you started. Hopefully it will help you finish off the rest of the questions.

==========================================

Problem 1

{18, a, b, -3} is an arithmetic sequence or arithmetic progression (AP).

This means we have some number d added on to each term to get the next term.

first term = 18

second term = first term + d = 18+d = a

third term = second term + d = (18+d)+d = 18+2d = b

fourth term = third term + d = (18+2d)+d = 18+3d = -3

----

Let's solve that last equation for d

18+3d = -3

18+3d-18 = -3-18

3d = -21

3d/3 = -21/3

d = -7

----

The value d = -7 tells us to add -7 to each term to get the next term. In other words, we subtract 7 from each term to get the next term

first term = 18

second term = first term + d = 18+d = 18+(-7) = 18-7 = 11

third term = second term + d = 11+d = 11+(-7) = 11-7 = 4

fourth term = third term + d = 4+d = 4+(-7) = 4-7 = -3

----

We see that a = 11 and b = 4 are the second and third terms respectively.

Therefore, a+b = 11+4 = 15

-------------

<h3>Answer: 15</h3>

==========================================

Problem 2

A multiple of 4 is in the form 4*n for some integer n, ie n is a whole number.

We want to know which values of 4*n are between 10 and 250.

----

Divide both 10 and 250 by 4 to get the following

10/4 = 2.5

250/4 = 62.5

If n = 2, then 4*n = 4*2 = 8 is not between 10 and 250; however n = 3 will make 4*n = 4*3 = 12 to be between 10 and 250. We see that n = 3 is the smallest possible allowed value.

If n = 62, then 4*n = 4*62 = 248 is between 10 and 250; while n = 63 will make 4*n too big because 4*63 = 252. The largest n can get is n = 62

----

The question posed in question 2 is equivalent to asking the following: "How many values are in the set {3, 4, 5, ..., 60, 61, 62}?"

You could count all of the values in the set, but that exercise is very tedious busywork. There's a much faster way. First lets consider the set below

{a, a+1, a+2, ..., b-2, b-1, b}

where a,b are integers. Basically this set starts at 'a', counts up until we get to 'b'. The handy formula

c = b-a+1

will provide the exact count of values in the set {a, a+1, a+2, ..., b-2, b-1, b}

----

In this case, a = 3 and b = 62, making

c = b-a+1

c = 62-3+1

c = 60

There are 60 values in the set {3, 4, 5, ..., 60, 61, 62}

There are 60 multiples of four that are between 10 and 250.

-------------

<h3>Answer: 60</h3>
4 0
3 years ago
Each person will eat 2/3 of a pound of Turkey and 8 people will be at party
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Each person will get 5.33 pound of turkey.
6 0
3 years ago
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One number is nine more than the other. Their sum is 33. Find the numbers.
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Answer: 12 21

Step-by-step explanation:

8 0
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*DIFFICULT QUESTION, PLEASE ANSWER ASAP * *MAKE SURE YOU PROVIDE DETAILS* Without knowing their diameters, which sporting ball h
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Answer:

Golf ball

Step-by-step explanation:

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