<span>The given function is ⇒⇒⇒ y = x² + 4x + 4 </span> 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
where r is radius and h is height