Question

Q1 : Find the inverse of the function.

f(x) = 7x - 1 (5 points)

Q2 : Find the inverse of the function.
f(x) = x3 - 7 (5 points)

Q3 : Find the inverse of the function.
f(x) = 5x3 - 3 (5 points)

Answer 1

1. Option D is correct.

2. Option B is correct.

3. Option B is correct.

Explanation:

Inverse function defined as the the function that undergoes the action of the other function.

A function
`f^(-1)` is the inverse of f if whenever y =f(x) and
`x =f^(-1)`

To find the inverse of the function:

Q1.

Given the function: f(x) = 7x -1

Put y for f(x) and solve for x;

y= 7x -1

Add 1 both sides we get;

y + 1 = 7x

Divide both sides by 7 we get;

`x = (y+1)/(7)`

Put
`f^(-1)(y)` for x;

`f^(-1)(y) = (y+1)/(7)`

Interchange y =x, we have

`f^(-1)(x) = (x+1)/(7)`

Q 2.

Given the function:

`f(x) = x^3 - 7`

Put y for f(x) and solve for x;

`y = x^3-7`

Add 7 both sides we get;

`y + 7 =x^3`

taking cube root both sides we get

`x =\sqrt[3]{y+7}`

Put
`f^(-1)(y)` for x;

`f^(-1)(y) =\sqrt[3]{y+7}`

Interchange y =x, we have

`f^(-1)(x) = \sqrt[3]{x+7}`

Q3 .

Given the function:

`f(x) = 5x^3 - 3`

Put y for f(x) and solve for x;

`y = 5x^3-3`

Add 3 both sides we get;

`y + 3 =5x^3`

Divide both sides by 5 we get;

`x^3 = (y+3)/(5)`

taking cube root both sides we get

`x = \sqrt[3]{(y+3)/(5) }`

Put
`f^(-1)(y)` for x;

`f^(-1)(y) = \sqrt[3]{(y+3)/(5) }`

Interchange y =x, we have

`f^(-1)(x) = \sqrt[3]{(x+3)/(5) }`