Find the inverse f (x) = (x-5) ^2

f - 1 (x) = √ x + 5, - √ x + 5

Step-by-step explanation:

To find the inverse, interchange the variables and solve for y

f⁻¹ (x) = ±√x + 5

Step-by-step explanation:

We have given a function.

f (x) = (x-5) ²

We have to find the inverse of given function.

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

y = (x-5) ²

Taking square root to both sides of above equation, we have

±√y = x-5

x = ±√y + 5

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

f⁻¹ (y) = ±√y + 5

Replace y with x, we have

f⁻¹ (x) = ±√x + 5 which is the answer.