Which of the following statements are true?

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))

sergejj [24]

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, f and g are inverses, then:

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

So, we can let j be the inverse function of h.

Function h is given by:

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

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for y. Add:

$\displaystyle x + 2 = 3y$

Hence:

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

Therefore, a = 1/3 and b = 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:

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

3 0

2 years ago

Help with this math homework

iren [92.7K]

Ranking in order from best to worst : Point, line, plane.

Step-by-step explanation:

12.A point in geometry is a location with no size and is shown by a dot. A point is the most fundamental object in geometry that represents a position.

A line can be defined as a connected set made up of infinitely many points.A line has one dimension and extends in infinitely in different directions.It has zero width and zero height.

A plane is an infinite set of points forming a connected flat surface that extends infinitely far in all directions. In a plane, the width, length and height are infinite.

13.

Points S and V are collinear points.

Points R, and U are collinear points

Points Q and T are collinear points

The figure has no plane indicated

Learn More

Point, line and plane : brainly.com/question/13148935

Keywords : line, plane, point, best worst, conclusion

#LearnwithBrainly

3 0

2 years ago

Joaquin has $1,300 in the bank and has investments worth $4,000. He also has $7,000 worth of credit card debt. What is Joaquin's

svetlana [45]

The answer to this question would be: -$1,700

In this question, we can separate the account into positive/debit and negative/credit value. The positive/debit value should be:

Joaquin has $1,300 in the bank
He has $4,000 worth of investment
Total positive value = $1300 + $4000= $5300

The negative value should be
$7,000 worth of credit card debt
Total positive value =$7000

Then the net worth should be: $5300 - $7000= -$1700

7 0

3 years ago

Chris shoots an arrow up into the air. The height (in feet) of the arrow is given by the function h(t) = - 16t2 + 64t + 112 wher

iris [78.8K]

Answer:

After 2 seconds

Step-by-step explanation:

First step is find an equation of velocity:

h(t)=-16t2+64t+112. The velocity function is derivated from position function, so we should do that.

v(t)= h´(t)= -16*2*t+64 ⇒ v(t)= -32t+64.

Now we know the arrow reach the maximun height when this velocity is equal to zero when t>0.

0=-32t+64 ⇒ 32t=64, split each member for 32 ⇒ $\frac{32t}{32}$ = $\frac{64}{32}$

t=2. That means after 2 sec. the arrow reach the maximum height

6 0

2 years ago

Read 2 more answers

What is the surface area of the prism?

Harman [31]

Area of lower rect + area of upper + 4 * sides rect areas

lower = upper rect

2 * rect1 + 4 * rect2

Area = 2 * 6 * 11 + 2 * 11 * 9 + 2 * 9 * 6 = 438 ft^2

or simply just take 2 ( and multiply each two sides.

5 0

2 years ago