Question

If f(x) =
`√(x) +3`, what is the equation for f–1(x)?

Answer 1

f⁻¹(x) = (x-3)²

Explanation:

We have given a function.

f(x) = √x + 3

We have to find inverse of above function.

f⁻¹(x) = ?

Putting y = f(x) in above equation, we have

y = √x + 3

We have to separate x from above equation.

Adding -3 to both sides of above equation, we have

y-3 = √x+3-3

y-3 = √x

Taking square to both sides of above equation, we have

(y-3)² = (√x)²

(y-3)² = x

Swapping above equation , we have

x = (y-3)²

Putting x = f⁻¹(y) in above equation, we have

f⁻¹(y) = (y-3)²

Replacing y with x , we have

f⁻¹(x) = (x-3)² which is the answer.

Answer 2

`f^(-1)(x) = x^(2)-6x+9` is the answer.

Explanation:

If the function is f(x) = √x + 3

We will write the function as an equation

y = √x + 3

√x = y - 3

x = (y -3)²

x = y² -6y +9

Now we will convert the equation into a function

`f^(-1)(x) = x^(2)-6x+9`

Therefore the inverse function f(x) = x²-6x+9