Question

Consider function f. f(x) = sqrt 7x- 21

Place the steps for finding f^-1(x) in the correct order.
please help:)​

Answer 1

The calculated inverse of the function
`\text{f(x)} = \sqrt{7x - 21` is
`f^(-1)(x) = (x^2)/(7) + 3`

How to determine the inverse of the function

From the question, we have the following parameters that can be used in our computation:

`\text{f(x)} = \sqrt{7x - 21`

Express the function as an equation

So, we have

`\text{y} = \sqrt{7x - 21`

Swap the variables x and y

This gives

`\text{x} = \sqrt{7y - 21`

Square both sides

`7y - 21 = x^2`

So, we have

`7y = x^2 + 21`

Divide through by 7

`y = (x^2)/(7) + 3`

Express as an inverse function

`f^(-1)(x) = (x^2)/(7) + 3`

Hence, the inverse of the function is
`f^(-1)(x) = (x^2)/(7) + 3`

Answer 2

f^-1(x) = (x² + 21)/7

Explanation:

Since f(x) = y = √(7x – 21), to find the inverse of f(x) we have to write x in terms of y in order to make x the dependent variable and y the independent variable. The steps involved are:

Step 1: square both sides of the equation, y = √(7x – 21). Doing that, we have:

y² = 7x – 21

Step 2: Add 21 to both sides of the resulting equation. Doing that, we have:

y² + 21 = 7x

Step 3: Divide both sides of the equation by 7. Doing that we have:

x = (y² + 21)/7

Step 4: Replace x with f^-1(x) and y with x. Doing that, we have:

f^-1(x) = (x² + 21)/7