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
bonufazy [111]
3 years ago
8

Find the inverse of the following function. Then prove they are inverses of one another.

Mathematics
1 answer:
solmaris [256]3 years ago
8 0

Answer: \dfrac{x^2+1}{2}

Step-by-step explanation:

Given

f(x)=\sqrt{2x-1}

We can write it as

\Rightarrow y=\sqrt{2x-1}

Express x in terms of y

\Rightarrow y^2=2x-1\\\\\Rightarrow x=\dfrac{y^2+1}{2}

Replace y be x to get the inverse

\Rightarrow f^{-1}(x)=\dfrac{x^2+1}{2}

To prove, it is inverse of f(x). f(f^{-1}(x))=x

\Rightarrow f(f^{-1}(x))=\sqrt{2\times \dfrac{x^2+1}{2}-1}\\\\\Rightarrow f(f^{-1}(x))=\sqrt{x^2+1-1}\\\\\Rightarrow f(f^{-1}(x))=x

So, they are inverse of each other.

You might be interested in
PLZZZHELPPSPSPSO
RUDIKE [14]
  • a) 2w-3 = 2(w+5)

Where w is width.

\huge\mathsf\colorbox{white}{}

  • b) 2x3 < n

Where n is the number

\huge\bold{\purple{\bold{⚡BeBrainly⚡}}}

3 0
3 years ago
The function f(x) = x2 is shifted up five units. Which of the following function equations represents this translation?
adelina 88 [10]
I think it’s b but i’m not sure
8 0
3 years ago
If i had 18 trees to cut and i finished 12 what percent did i cut
mixer [17]
You would have 14.76 trees cut
4 0
3 years ago
Read 2 more answers
a system of equations is shown below: x y = 3 2x − y = 6 the x−coordinate of the solution to this system of equations is _____.
pychu [463]
If you would like to solve the system of equations x + y = 3 and 2x - y = 6, you can do this using the following steps:

<span>x + y = 3 ... y = 3 - x
2x - y = 6
</span>_________
<span>2x - y = 6
</span>2x - (3 - x) = 6
2x - 3 + x = 6
3x = 6 + 3
3x = 9     /3
x = 9/3
x = 3

<span>y = 3 - x = 3 - 3 = 0
</span>
The correct result would be x = 3.
6 0
3 years ago
What is the measure of A 54°<br> D. 66°<br> B. 56°<br> E. 114°<br> C. 58°
dangina [55]

Answer:

66 I think might he wrong

Step-by-step explanation:

I'm not sure if its right

5 0
3 years ago
Read 2 more answers
Other questions:
  • The diagonal of a square is 15 inches. find the area of the square
    13·1 answer
  • What is the common difference or common ratio of the sequence 2, 5, 8, 11, ...?
    6·2 answers
  • A bicycle, a motorcycle, a sports car, and a garbage truck are stuck on the side of the
    15·2 answers
  • The figure shows two perpendicular lines s and r, intersecting at point P in the interior of a trapezoid. Line r is parallel to
    10·1 answer
  • A missing fraction on a number line is located exactly halfway between 3/6 and 5/6. what is the missing fraction
    7·2 answers
  • For each of the following pairs of signed integers (2’s complement), subtract the second from the first. Show the decimal equiva
    10·1 answer
  • Alec paid the bill for dinner with his clients which totaled $140 before tax and tip. If an 8 percent sales tax was added to the
    13·1 answer
  • Given the statement “If a line is horizontal, then it has slope equal to zero,” what is its contrapositive?
    6·1 answer
  • 1. A flower arrangement has seven carnations and 21 daffodils. What is the ratio of carnations to daffodils in the arrangement?
    9·2 answers
  • A town doubles its size every 64 years. If the population is currently 1700, what will the population be in 128 years.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!