Q:

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

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

Accepted Solution

A:
Answer: 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 equationy = (x+2)(x+2)y = (x+2)²         ⇒⇒⇒ take the square root to both sides√y = x+2x = √y - 2         ⇒⇒⇒ x becomes a function of yfinal step:∴ y = √x - 2   ⇒⇒⇒ the inverse of the given functionSo, as a conclusion:f(x) = y = x² + 4x + 4  ⇒⇒⇒ the given functionf⁻¹(x) = y = √x - 2       ⇒⇒⇒ the inverse of the given function Find the inverse of the function. y=x2+4x+4 6504825e75d0c.webp