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
neonofarm [45]
2 years ago
13

Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

Mathematics
1 answer:
sergejj [24]2 years ago
3 0

Answer:

\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, <em>f</em> and <em>g</em> are inverses, then:

\displaystyle f(g(x)) = g(f(x)) = x

So, we can let <em>j</em> be the inverse function of <em>h</em>.

Function <em>h</em> is given by:

\displaystyle h(x) = y = 3x-2

Find its inverse. Flip variables:

x = 3y - 2

Solve for <em>y. </em>Add:

\displaystyle x + 2 = 3y

Hence:

\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}

Therefore, <em>a</em> = 1/3 and <em>b</em> = 2/3.

We can verify our solution:

\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}

And:

\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x  \stackrel{\checkmark}{=} x\end{aligned}

You might be interested in
Subtract these polynomials.
Artist 52 [7]

Answer:

The correct answer is D. 3x² - x + 3

Step-by-step explanation:

4x² - x + 6 - (x² + 3)

= 4x² - x² - x + 6 - 3

= 3x² - x + 3

5 0
3 years ago
Write and solve an inequality.
TEA [102]

Answer:

ok

Step-by-step explanation:

4 0
2 years ago
El numero de libros vendidos en una tienda aumentó aproximadamente de 6000 a 9000 durante varios meses cual porcientorepresenta
Aleksandr-060686 [28]

Answer:

50%

Step-by-step explanation:

To calculate the percentage of increase, what we must do divide the two quantities, in this way we will be able to know how bigger they are from each other. So:

9000/6000 = 1.5

Now, we subtract those from 1, which would be 100%

1.5 - 1 = 0.5

therefore the increase was 50%

6 0
3 years ago
What are the comon factors of 70&amp;20??
Musya8 [376]
70: 1,2,5,7,10,14,35,<span>70
20: 1,2,4,5,10,20</span>
3 0
3 years ago
Evaluate |x|+(-2x^2) for x=3<br> Answers<br> -9<br> -15<br> 21
Nikolay [14]

Hello from MrBillDoesMath!

Answer:

-15

Discussion:

We are asked to evaulate:

abs(3) + ( -2 (3)^2) =                         => as abs(3) = 3

3          + (-2*9)  =

3           - 18 =

-15    

Thank you,

MrB

8 0
3 years ago
Other questions:
  • Which of the following are even numbers ?
    9·1 answer
  • Which statement is the correct interpretation of the inequality -3&gt; -4?
    7·2 answers
  • Find the LCM of the set of numbers 4 5 6
    10·2 answers
  • The heights of adult females are normally distributed. If you were to construct a histogram of 40 randomly selected​ women, what
    7·1 answer
  • Translation is a congruency transformation. True or false
    10·2 answers
  • If f(x) = 3/x + 2 - x-3, complete the following statement ( round your answer to the nearest hundredth):
    8·2 answers
  • Solve the equation.<br><br> −10=−b4
    11·2 answers
  • Find the exact values of sin (-pi/12)
    15·2 answers
  • HELP THIS IS DUE IN 15 MINUTE AND I DONT KNOW HOW TO SOLVW IT
    5·1 answer
  • Questions What is an amount between $2 and $10? (A) __________ What is an amount between $10 and $20? (B) __________ What is an
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!