MATH SOLVE

2 months ago

Q:
# 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