What’s the slope of this line?

4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail

Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

$h^{-1}(x)=\sqrt{\frac{x+1}{3}}$ ⇒ answer D

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = $f^{-1}(x)$

* Lets use these steps to solve the problems

∵ $f(x)=\sqrt{x-3}$

∵ f(x) = y

∴ $y=\sqrt{x-3}$

- Exchange x and y

∴ $x=\sqrt{y-3}$

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by $f^{-1}(x)$

∴ $f^{-1}(x)=x^{2}+3$

∵ g(x) = x² + 3

∴ $f^{-1}(x)=g(x)$

∴ The functions are inverses to each other

* Now lets find f(g(x))

- To find f(g(x)) substitute x in f(x) by g(x)

∵ $f(x)=\sqrt{x-3}$

∵ g(x) = x² + 3

∴ $f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x$

∴ f(g(x)) = x

∴ The functions are inverses; f(g(x)) = x

* Lets find the inverse of h(x)

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ $\frac{x + 1}{3}=y^{2}$

- Take √ for both sides

∴ ± $\sqrt{\frac{x+1}{3}}=y$

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ $\sqrt{\frac{x+1}{3}}=y$

- replace y by $h^{-1}(x)$

∴ $h^{-1}(x)=\sqrt{\frac{x+1}{3}}$

4 0

3 years ago

Christiana and Marlena opened their first savings accounts on the same day. Christiana opened her account with $55 and plans to

PolarNik [594]

Answer: it will take 4 months for the amount to be the same and the amount would be $95

Step-by-step explanation:

Let x represent the number if months it will take for the two accounts have the same amount of money.

Christiana opened her account with $55 and plans to deposit $10 every month. This means that the amount that in the account after x months would be

10x + 55

Marlena opened her account with $35 and plans to deposit $15 every month. This means that the amount that in the account after x months would be

15x + 35

For the amount in the accounts to be the same, the number of months would be

15x + 35 = 10x + 55

15x - 10x = 55 - 35

5x = 20

x = 20/5

x = 4

The amount would be

15 × 4 + 35

= 60 + 35

= $95

8 0

3 years ago

Read 2 more answers

if max has pens 400 and he adds 700 how much will he have? pls plsssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss

insens350 [35]

Answer:

so basically first add 700+300 which would come up to 1000. 300+100 is 400 so add 100 to the 1000 and you have 1100

4 0

2 years ago

Tuna provides 30 calories per ounce . On a graph representing the relationship between the number of ounces of tuna a person con

Rama09 [41]

Ounces of tuna will go on the x axis and calories on the y axis. This is because the relationship between the number of ounces a person eats and the calories he consumes then is a positive correlation (a line with a positive slope which goes from lower left to upper right) with x being the independent variable. As x increases, y increases. In other words you can ONLY change the amount of calories you consume WHEN you change the amount of ounces you eat. You can't change the number of calories independent of the number of ounces. The independent variable goes along the x axis, cuz the x variable always represents the independent variable.

5 0

3 years ago

Read 2 more answers

Find the area of the figure. I need help please

Vesna [10]

Answer:24 + 24 = 48

you multiply the lenth and with for each of the rectangles

4 0

3 years ago