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
Leto [7]
3 years ago
8

Which of the following pairs of functions are inverse of each other ?

Mathematics
2 answers:
pshichka [43]3 years ago
5 0
One way is to solve for the invers of the first function
remembe, to solve, replace f(x) or g(x) with y, switch x and y, solve for y and replace it with f⁻¹(x)

A.
f(x)=x/2+8
y=x/2+8
x=y/2+8
x-8=y/2
2x-16=y
f⁻¹(x)=2x-16
nope, not A


B.
f(x)=3x³+16
y=3x³+16
x=3y³+16
x-16=3y³
(x-16)/3=y³
∛((x-16)/3)=y
f⁻¹(x)=∛((x-16)/3)
nope, not the same
not B

C.
f(x)=18/x-9
y=18/x-9
x=18/y-9
x+9=18/y
y(x+9)=18
y=18/(x+9)
f⁻¹(x)=18/(x+9)
correct, the answer is C



answer is C
zaharov [31]3 years ago
5 0

Option C.

<h3>Further explanation</h3>

To find the formula for the inverse of a function, solve the equation y = f(x) for x and interchange x and y.

Let's examine the options one by one.

<u>[Option A]</u>

\boxed{ \ f(x) = \frac{x}{2} + 8 \ } \ and \ \boxed{ \ g(x) = 2x - 8 \ }

In the equation y = f(x), both sides are subtracted by 8.

\boxed{ \ y - 8 = \frac{x}{2} \ }

\boxed{ \ \frac{x}{2} = y - 8 \ }

Both sides are multiplied by 2.

\boxed{ \ x = 2(y - 8) \ }

\boxed{ \ x = 2y - 16 \ }

Let's replace \boxed{x \ with \ f^{-1}(x)} \ and \ \boxed{y \ with \ x}.

Thus, the inverse of \boxed{ \ f(x) = \frac{x}{2} + 8 \ } \ is \ \boxed{\boxed{ \ f^{-1}(x) = 2x - 16 \ }}

Therefore f(x) and g(x) are not pairs of functions that inverses of each other.

<u>[Option B]</u>

\boxed{ \ f(x) = 3x^3 + 16 \ } \ and \ \boxed{ \ g(x) = \sqrt[3]{\frac{x}{3}} - 16 \ }

In the equation y = f(x), both sides are subtracted by 16.

\boxed{ \ y - 16 = 3x^3 \ }

\boxed{ \ 3x^3 = y - 16 \ }

Both sides are divided by 3.

\boxed{ \ x^3 = \frac{y - 16}{3} \ }

Next, eliminate the cube on the variable by taking the cube root of both sides of the equation.

\boxed{ \ x = \sqrt[3]{\frac{y - 16}{3}} \ }

\boxed{ \ x = \sqrt[3]{ \frac{y}{3} - \frac{16}{3}} \ }

Let's replace \boxed{x \ with \ f^{-1}(x)} \ and \ \boxed{y \ with \ x}.

Thus, the inverse of \boxed{ \ f(x) = 3x^3 + 16 \ } \ is \ \boxed{\boxed{ \ f^{-1}(x) = \sqrt[3]{ \frac{x}{3} - \frac{16}{3}} \ }}

Therefore f(x) and g(x) are not pairs of functions that inverses of each other.

<u>[Option C]</u>

\boxed{ \ f(x) = \frac{18}{x} - 9 \ } \ and \ \boxed{ \ g(x) = \frac{18}{x + 9} \ }

In the equation y = f(x), both sides are added by 9.

\boxed{ \ y + 9 = \frac{18}{x} \ }

Both sides are multiplied by x and divided by (y + 9) or a crossing occurs between x and (y + 9).

\boxed{ \ x = \frac{18}{y + 9} \ }

Let's replace \boxed{x \ with \ f^{-1}(x)} \ and \ \boxed{y \ with \ x}.

Thus, the inverse of \boxed{ \ \frac{18}{x} - 9 \ } \ is \ \boxed{\boxed{ \ f^{-1}(x) = \frac{18}{x + 9}} \ }}

Therefore, f(x) and g(x) correctly attend pairs of functions that inverses of each other.

<u>[Option D]</u>

To be more skilled, we still eager to properly check Option D.

\boxed{ \ f(x) = 8x^3 - 10 \ } \ and \ \boxed{ \ g(x) = \frac{x^3 + 10}{8} \ }

In the equation y = f(x), both sides are added by 10.

\boxed{ \ y + 10 = 8x^3 \ }

\boxed{ \ 8x^3 = y + 10 \ }

Both sides are divided by 8.

\boxed{ \ x^3 = \frac{y + 10}{8} \ }

Next, eliminate the cube on the variable by taking the cube root of both sides of the equation.

\boxed{ \ x = \sqrt[3]{\frac{y + 10}{8}} \ }

As usual, let's replace \boxed{x \ with \ f^{-1}(x)} \ and \ \boxed{y \ with \ x}.

Thus, the inverse of \boxed{ \ f(x) = 8x^3 - 10 \ } \ is \ \boxed{\boxed{ \ f^{-1}(x) = \sqrt[3]{\frac{x + 10}{8}} \ }}

Therefore f(x) and g(x) are not pairs of functions that inverses of each other.

<h3>Learn more</h3>
  1. The inverse of a function brainly.com/question/3225044  
  2. If g(x) is the inverse of f(x), what is the value of f(g(2))? brainly.com/question/1517760
  3. The composite function brainly.com/question/1691598  

Keywords: which of the following pairs of functions, the inverse of each other, replace, the equation, eliminate the cube on the variable, by taking the cube root of both sides, f(x), g(x)

You might be interested in
Which of the following rates is proportional to $2.50 for 5 cans?
MAVERICK [17]
A, divide 2.5 by 5 and you get 0.5, multiply that by 9 and you get 4.5. A is the answer
4 0
3 years ago
Read 2 more answers
74 rounded to the nearest hundreth
WARRIOR [948]
100 would be your answer
7 0
3 years ago
a recipe for cookies calls for 3/5 of a cup of brown sugar and make 6 cookies if you adjust the recipe to make a cookies how muc
sineoko [7]
Find 3/5 in a decimal and it 6 to get 0.6 + 6 + 6.6 then convert it back to a fraction and you have c cups and 3/5 cup
4 0
3 years ago
1, -c/2 &lt; -1.5<br> 2. -y/2 &lt; 6<br> 3. -d/3 &gt; -9
irina1246 [14]

Answer:

um ight if your asking me if there are right i guess they are...

3 0
2 years ago
Whats 123456+65432134
Flauer [41]

Answer:65555590

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Other questions:
  • A bike and helmet worth $320. The bike is 7 times more than helmet. Find the value
    11·2 answers
  • How do you simplify a fraction when the numerator is bigger than the denominator.
    6·2 answers
  • Solve for r:<br><br> -5 = 7 + 3r
    11·2 answers
  • The trinomial x2 – 3x – 4 is represented by the model.
    10·1 answer
  • A police officer claims that the proportion of accidents that occur in the daytime (versus nighttime) at a certain intersection
    8·1 answer
  • What is the solution to the problem?
    11·1 answer
  • Given the point (4,5) and the slope is 6, find y when x=24
    15·2 answers
  • Students in a pre-algebra class are given the polynomial 12x2y−6xy+18y2 and told to factor out the greatest common factor. Which
    9·1 answer
  • For school lunch students have 3 meat choices (beef, chicken, or fish), 2 potato choices (mashed or fried), and 3 drink choices
    14·2 answers
  • Actorize Completely PQ+ PR - RQ -Q²​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!