4th time asking ! me! someone . i need the correct answers. i don’t want to fail

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

⇒ 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 =

* Lets use these steps to solve the problems

∵

∵ f(x) = y

∴

- Exchange x and y

∴

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by

∴

∵ g(x) = x² + 3

∴

∴ 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)

∵

∵ g(x) = x² + 3

∴

∴ 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

∴

- Take √ for both sides

∴ ±

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴

- replace y by

∴

.

step-by-step explanation:

.

7.3

step-by-step explanation: