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
Use the graph to state the solution for the system. (In other words, what is the solution for the system?)
timurjin [86]
(2,1) is the solution because its where they both intersect..
3 0
3 years ago
x + 3y = 7 x - 3y = 1 Solve the system of equations. A) x = 4, y = 1 B) x = 1, y = 4 C) x = - 2 3 , y = 3 D) x = 3, y = - 2 3
Alik [6]
X+3y=7
x-3y=1
add them together

x+3y=7
<u>x-3y=1 +
</u>2x+0y=8

2x=8
divide 2
x=4
subsitute
x+3y=7
4+3y=7
subtract 4
3y=3
divid 3
y=1

x=4
y=1

answer is A
<u />
6 0
3 years ago
Read 2 more answers
A contractor is given a scale drawing of a rectangular patio. The scale from the patio to the drawing is 4ft to 1in. What is the
AnnyKZ [126]

Answer:

170 ft²

Step-by-step explanation:

Given:

Patio drawing of 4.25 in by 2.5 in

Scale of Patio to its drawing = 4ft to 1 in

Requires:

Area of actual Patio

SOLUTION:

Area of actual Patio = area of a rectangle = length × width

Given a scale drawing of 4ft to 1 in, therefore:

Length of actual Patio = 4.25 × 4 = 17 ft

Width of actual Patio = 2.5 × 4 = 10 ft

Therefore:

Area of actual Patio = 17 ft × 10 ft = 170 ft²

5 0
2 years ago
If x^3=216, what is the value of x?​
sleet_krkn [62]

Answer:

6

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Why is cosine positive in the 4th quadrant and sine isn’t?
kari74 [83]

Answer:

Because sine can only be positive in quadrant II according to the CAST rule.

8 0
3 years ago
Other questions:
  • Is 419108 divisible by 4?
    10·2 answers
  • Please look at the picture first!
    10·2 answers
  • Find Solution Asap BRANLIEST ​
    5·1 answer
  • FeCl3 + O2  Fe2O3 + Cl2 BALANCE the equation
    11·1 answer
  • A business wants to manufacture refridgerators. Before they start production, they need to make sure they can make a profit with
    6·1 answer
  • Based on the line of best fit, how much money would a company most likely spend on advertising if the company's yearly revenue w
    9·2 answers
  • A local school donated canned goods to help the community. Cans were packed into boxes each weighing 16.4 pounds. The volunteers
    11·2 answers
  • Perimeter of a rectangle is 72 inches. The width is twice
    8·2 answers
  • Consider the following formula used to find the volume of a cone.
    12·2 answers
  • Please help me with this question
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!