Find the inverse of the function. y = x2 + 4x + 4

The given function is ⇒⇒⇒ y = x² + 4x + 4

To find the inverse of the function, we need to make x as a function of y and at the final step make a switch between x and y (i. e. make x as y and y as x)

y = x² + 4x + 4 ⇒⇒⇒ factor the quadratic equation

y = (x+2) (x+2)

y = (x+2) ² ⇒⇒⇒ take the square root to both sides

√y = x+2

x = √y - 2 ⇒⇒⇒ x becomes a function of y

final step:

∴ y = √x - 2 ⇒⇒⇒ the inverse of the given function

So, as a conclusion:

f (x) = y = x² + 4x + 4 ⇒⇒⇒ the given function

f⁻¹ (x) = y = √x - 2 ⇒⇒⇒ the inverse of the given function