1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
KatRina [158]
3 years ago
14

If f(g(x)) = g(f(x)) = x, and g(x) = 2 + In(x + 1), find f(4).

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
5 0

If f(g(x))=g(f(x))=x, then g and f are inverses of one another. So we know g(f(4))=4.

g(f(4))=2+\ln(f(4)+1)=4

\implies\ln(f(4)+1)=2

\implies f(4)+1=e^2

\implies\boxed{f(4)=e^2-1}

You might be interested in
you bought 5 chocolate bars and 8 blow pops for $23.25 your sister bought 2 chocolate bars and 13 blow pops for 21.55 how much d
kirza4 [7]

Answer:

  • $2.65

Step-by-step explanation:

Let chocolate bar = c and blow pops = b

<u>As per given we have equations below:</u>

  • 5c + 8b = 23.25
  • 2c + 13b = 21.55

<u>13 times the first equation minus 8 times the second to eliminate b and find c:</u>

  • 13(5c + 8b) - 8(2c + 13b) = 13(23.25) - 8(21.55)
  • 65c - 16c = 129.85
  • 49c = 129.85
  • c = 129.85/49
  • c = 2.65

Each chocolate bar costs $2.65

7 0
3 years ago
-8 - (-15) + 30 equals​
Phantasy [73]

The answer to your problem is 11

8 0
3 years ago
A town has a population of 8000 and grows at 3% every year. To the nearest tenth of a year, how long will it be until the popula
Alexxx [7]

Answer:

It will take approximately 34 years

Step-by-step explanation:

If a town population is 8000 and grows 3% annually.

How long will it take to reach 16300

growth is 16300 - 8000 = 8300

using simple interest formula

SI = (P × r × t)/100

8300 = (8000 × 3 × t)100

8300= (80 × 3)t

8300 = 240t

t = 8300/240

t ≈ 34 years to the nearest tenth

8 0
3 years ago
The length of the rectangle is 7/(x-4) feet, while its width is 5/x feet. Find its perimeter. Please help asap!!!!! :(
damaskus [11]

The perimeter would be (24x - 40)/(x^2 - 4x).

In order to find this, first double the length and width as you would to find any perimeter.

7/(x - 4) * 2 = 14/(x - 4)

5/x * 2 = 10/x

Now to add those together, we need to give them common denominators. In order to do that with the first one, we need to multiply by x/x

14/(x - 14) * x/x = 14x/(x^2 - 14x)

Then we can do the same with the second part by multiplying by (x - 4)/(x - 4)

10/x * (x - 4)/(x - 4) = (10x - 40)/(x^2 - 14x)

Now we can add the two together

14x/(x^2 - 14x) + (10x - 40)/(x^2 - 14x) = (24x - 40)/(x^2 - 14x)

3 0
3 years ago
Pay no attention to the stuff I wrote please
pychu [463]
What's your question?
7 0
3 years ago
Other questions:
  • Simplify completely 14x^5y^4/21x^3y^2/7x^3y.
    15·1 answer
  • which second degree polynomial function has a leading coefficient of -1 an root 4 with multiplicity 2?
    13·2 answers
  • Plz help me what this means I’m so confused
    13·1 answer
  • Write the polynomial in standard form. Then name the polynomial based on it's degree and number of terms.
    13·2 answers
  • 3 When 25 x+2y-* x-12y+3) x-1ży+3) is simplified, what is the resulting expression? 1 Tox+23y+6 7. x+23y+6 x+85y+8 1 Tox+4*x+3​
    6·1 answer
  • (4,1) &amp; (6, 7)<br> Write the equation in point slope form
    8·2 answers
  • You roll a number cube and flip a coin. What is the probability of rolling a number less than 5 and flipping heads?
    12·1 answer
  • 1. In order to draw a straight vertical line segment that is 4 units long, which point must be connected to (1, 2)?
    10·1 answer
  • Write money amounts using a leading zero if necessary &amp; with 2 decimal places (For example: 0.80 or 0.72 or 1.23)
    6·1 answer
  • What is the average rate of change for this quadratic function for the interval fr x=2 to x=4?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!