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
12345 [234]
3 years ago
10

If the function f(2x + 3) = 3x- 8, find f -¹(x)​

Mathematics
2 answers:
bagirrra123 [75]3 years ago
7 0

Answer:

Step-by-step explanation:

let~g(x)=2x+3,~ then~f\circ g(x)=f(g(x)=3x-8\\\\

lets assume that f(x) is a line, so f(x)=mx+b

f(g(x))=m(2x+3)+b=2mx+3m+b=3x-8

the follow equation system results:

2m=3 \\ 3m+b=-8

m=\frac{3}{2}\\\\b=-\frac{25}{2}

finally:

y=f(x)=\frac{3}{2}x-\frac{25}{2}

now is time to calculate the inverse function:

y=\frac{3}{2}x-\frac{25}{2}=>2y+25=3x=>x=\frac{2}{3}y+\frac{25}{3}

so

f^{-1}(x)=\frac{2}{3}x+\frac{25}{3}

Bumek [7]3 years ago
3 0

Answer:

(2x + 35)/3

Step-by-step explanation:

f(2x + 3) = 3x - 8

= 3(2x)/2 - 8

= 3(2x + 3 - 3)/2 - 8

= 3(2x + 3)/2 - 3(3)/2 - 8

= ( 3(2x + 3) - 25)/2

Therefore, f(x) = (3x - 25)/2

Let f(x) = (3x - 25)/2 = y

Therefore,

x = (2y + 35)/3 = f(y)

Hence,

f-¹(x) = f(y) = (2y + 35)/3

Just by merely replacing y,

f-¹(x) = (2x + 35)/3

You might be interested in
If the simple interest rate is 5%p.a. , how long does it take for the amount to become twice the principal
solong [7]
A = P + I
2a = a + PTR/100
2a = a + 5aT/100
2a = a(1+T/20)
2=1+T/20
T=20 yrs

3 0
3 years ago
Use the distributive property to simplify the following expression: 3y(2 - y) + 8y
Debora [2.8K]
3y(2 - y) + 8y
6y - 3y^2 + 8y
-3y^2 + 14 y
5 0
3 years ago
Imagine that you are standing at the top of a cliff that is 1,500 feet above sea level. You see ship A, and your eyes make an an
kati45 [8]
Answer: option A. 30 °.

Explanation:

1) Draw this triangle: Eyes - Ship A - height of the cliff:

The angle of the vertix where the eyes are is: 90° - depreesion angle = 90° - 60° = 30°.

2) opossite leg = horizontal distance to the ship A = x

3) adjacent leg = height of the cliff = 1500 feet

4) tan(30°) = x / 1500 feet => x = 1500 tan(30°) = 1500 √3 / 3 = 500√3

5) Draw the triangle of the eyes - ship B - hieght of the cliff

6) The unknown is the depression angle of the eyes with ship B, α

7) opposite leg = 500√3 feet + 1000√3 feet = 1500√3 feet

8) adjacent leg = height of the cliff = 1500 feet

9) tan(α) = opposite leg / adjacent leg = 1500√3 / 1500 = √3

10) α = arctan(√3) = 60°

11) Depression angle = 90° - 60° = 30° Which is the answer

5 0
3 years ago
Read 2 more answers
Given a circle with a circumference of 10cm, which equation shows how the relationship between a circumference and its diameter
sweet-ann [11.9K]

Answer:

D

Step-by-step explanation:

Multiply the circumference by the diameter which is D

3 0
3 years ago
No Spam!!!! I will mark brainliest whoever properly answers the question. Identify the binomial that is a factor of the polynomi
Anestetic [448]

Answer:

4.78x

Step-by-step explanation:

how've 7,.8*x 3n by 6y is =4.78x

3 0
3 years ago
Other questions:
  • Complete the solution of the equation. find the value of y when x equals 4 -3x +9y = -57
    11·1 answer
  • PLS HELP HELP HELP HELP HELP
    15·2 answers
  • A small country consist of four states the population of state Inc. is 67,200 the population of CB is 78,300 the population of s
    11·1 answer
  • Which table of values contains only points that lie on the line represented by this equation?​
    8·1 answer
  • In a group of 33 students, 7 study both Art and Biology. 10 study Biology but not Art. 7 study neither subject. How many study A
    12·1 answer
  • Given the two expressions shown below:
    7·2 answers
  • Write the fraction in lowest terms.<br> 2/19
    11·1 answer
  • Resultado de (+23) – (-34)
    9·2 answers
  • Convert 88% to a fraction.<br> a 1/8<br> b 22/25<br> c 23/50<br> d 22/55
    13·1 answer
  • A ladder is leaning against a building as shown in the
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!