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
marishachu [46]
3 years ago
8

PLEASE HELP!!!! Which of these pair of functions are inverse functions?

Mathematics
1 answer:
Mamont248 [21]3 years ago
3 0

Answer:

Option B and C are correct.

Step-by-step explanation:

Inverse function: If both the domain and the range are R for a function f(x), and if f(x) has an inverse g(x) then:

f(g(x)) = g(f(x)) = x for every x∈R.

Let f(x) = \frac{1}{2}(\ln(\frac{x}{2}) -1) and g(x) = 2e^{2x+1}

Use logarithmic rules:

  • ln e^a = a
  • e^{lnx} = x
  • \ln a^b = b\ln a

then, by definition;

f(g(x)) = f(2e^{2x+1}) =\frac{1}{2}(\ln(\frac{2e^{2x+1}}{2})-1) = \frac{1}{2}(\ln(e^{2x+1}}){-1) = \frac{1}{2} (2x+1-1) =\frac{1}{2}(2x) = x

g(f(x)) = g(\frac{1}{2}(\ln(\frac{x}{2}) -1)) = 2e^{2({\frac{1}{2}(\ln(\frac{x}{2}) -1})+1 2e^{(\ln(\frac{x}{2}) -1+1}=2e^{\ln(\frac{x}{2})} =2\cdot \frac{x}{2} = x

Similarly;

for f(x) = \frac{4 \ln(x^2)}{e^2} and g(x) = e^{\frac{e^2 \cdot x}{8} }

then, by definition;

f(g(x)) = f(e^{\frac{e^2 \cdot x}{8}}) =\frac{4 \ln {(\frac{e^2 \cdot x}{8})^2}}{e^2} = \frac{8 \ln {(\frac{e^2 \cdot x}{8})}}{e^2} =\frac{8\frac{e^2\cdot x}{8} }{e^2}=\frac{8e^2 \cdot x}{8e^2}=x

Similarly,

g(f(x)) = x

Therefore, the only option B and C are correct. As the pairs of functions are inverse function.

You might be interested in
Sorting Quadratic Function Discriminants
nataly862011 [7]

The number of zeros of the quadratic functions, considering their discriminant, is given as follows:

  • discriminant = 0: 1 Real number solution.
  • discriminant = -36: 0 Real number solutions.
  • discriminant = 3: 2 Real number solutions.
  • discriminant = 2: 2 Real number solutions.
  • discriminant = 100: 2 Real number solutions.
  • discriminant = -4: 0 Real number solutions.

<h3>What is the discriminant of a quadratic equation and how does it influence the solutions?</h3>

A quadratic equation is modeled by:

y = ax^2 + bx + c

The discriminant is:

\Delta = b^2 - 4ac

The solutions are as follows:

  • If \mathbf{\Delta > 0}, it has 2 real solutions.
  • If \mathbf{\Delta = 0}, it has 1 real solutions.
  • If \mathbf{\Delta < 0}, it has 0 real solutions.

Hence, for the given values of the discriminant, we have that:

  • discriminant = 0: 1 Real number solution.
  • discriminant = -36: 0 Real number solutions.
  • discriminant = 3: 2 Real number solutions.
  • discriminant = 2: 2 Real number solutions.
  • discriminant = 100: 2 Real number solutions.
  • discriminant = -4: 0 Real number solutions.

More can be learned about quadratic functions at brainly.com/question/24737967

#SPJ1

5 0
1 year ago
A segment in the complex plane has a midpoint at 3 – 2i. If one endpoint of the segment is at 7 i, what is the other endpoint? –
Brut [27]

The midpoint of a segment divides the segment into equal halves

The other endpoint is 1- 5i

<h3>How to determine the missing endpoint </h3>

The coordinates are given as:

Point 1: 7 + i

Midpoint: 3 - 2i

Represent the other endpoint with x.

So, we have:

2 * Midpoint = Point 1 + x

This gives

2 * (3 - 2i) =7 + i + x

6 - 4i =7 + i + x

Collect like terms

x = 6 -7- 4i -i

Evaluate the like terms

x = 1- 5i

Hence, the other endpoint is 1- 5i

Read more about midpoints ta:

brainly.com/question/9635025

6 0
1 year ago
Can someone help please 3x-y=13 A. (6,5) B.(3,-4) C. (6,5) and (3,-4) D. neither
gavmur [86]

Answer:

C. (6, 5) and (3, -4)

Step-by-step explanation:

Given the equation 3x - y = 13, we need to figure out which points satisfy it. In order for an ordered pair to satisfy an equation, when we plug the x-coordinate in for x and the y-coordinate in for y, the equation should hold true.

Let's try with (6, 5):

3x - y = 13

3 * 6 - 5 =? 13

18 - 5 =? 13

13 = 13

Since this is true, we know that (6, 5) is indeed a solution.

Now let's try with (3, -4):

3x - y = 13

3 * (3) - (-4) =? 13

9 + 4 =?13

13 = 13

Again, since this is true, then (3, -4) must be a solution.

Thus, the answer is C.

<em>~ an aesthetics lover</em>

6 0
2 years ago
Read 2 more answers
What is the slope of a line perpendicular to y = -7/4x?
dexar [7]
A line is perpendiculat to another which has a slope of m if the perpendicular line has a slope of -1/m.
That means that if the product of slopes of two lines is -1, the two lines are perpendicular.

Here, y1=-7/4x, or m=-7/4
The perpendicular should have a slope of -1/m=-1/(-7/4)=4/7
6 0
3 years ago
Find the product <br> -1/2 y(2y3-8)
MissTica
0-(( \frac{1}{2} *y)*2y^3-8) \\ \\ then \ we \ would \ simplify \ 1/2 \\ \\ we \ factor y^3 - 4 \\ \\ 4 \ would \ not \ be \ a \ perfect \ cube. \\ \\ therefore, \ your \ answer \ would \ then \ be \ the \ following: \\ \\ \boxed{ -y * (y^3 - 4)}
8 0
3 years ago
Other questions:
  • Which words describe this shape? Mark all that apply.A polygon(B) open shapepentagonD quadrilateral
    7·2 answers
  • What is the answer to this this is very urgent ​
    8·1 answer
  • Estimate 23,945 + 46,718 by rounding to the highest place value.
    11·1 answer
  • write the ratio in simplest form. the hockey team played 82 regular season games last year. If they won 44 games, what is the ra
    9·1 answer
  • What is the average per day?
    14·2 answers
  • 4(3A - 4)=56 what is the variable for A?<br><br> Pls show the steps {Thanks}
    6·2 answers
  • The polygons are similar. Find the value of x and y.
    7·1 answer
  • What is the end behavior of the graph below ? (CHOOSE 2 ANSWERS)
    14·2 answers
  • 1. 0.000527 = 5.27 x 10-4<br><br> a. The number 0.000527 is a very<br><br> number.
    11·1 answer
  • Marcus is comparing the costs of two cellular phone services.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!