Question

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

Answer 1

f⁻¹(x) = (x-3)² is the inverse of given function.

Explanation:

We have given function:

f(x) =√x +3

W e have to find the inverse of the given function.

Let y = f(x) then

y = √x +3

First, we interchange x and y we get,

x =√y +3

then solve the above equation for y we get,

√y = (x-3)

Squaring both sides we get,

y= (x-3)²

Replacing y to f⁻¹(x) we get,

f⁻¹(x) = (x-3)² is the inverse of given function.

Answer 2

(x-3)^2

Explanation:

y = sqrt(x) +3

To find the inverse , we exchange x and y and then solve for y

Exchange x and y

x = sqrt(y) +3

Now solve for y

Subtract 3 from each side

x-3 = sqrt(y)

Square each side

(x-3)^2 = (sqrt(y))^2

(x-3)^2 = y

The inverse of sqrt(x) +3 is (x-3)^2