what is the inverse of the quadratic function f(x)=x^2+12x+37

Answer 1

f(x)=x^2+12x+37

y = x^2 + 12x + 37
Solve for x
x^2 + 12x = y - 37

Complete the square
x^2 + 12x + 36 = y - 37 + 36
(x + 6)^2 = y - 1

Take the square root of both sides
+- (x + 6) = (sqrt(y - 1))

x + 6 = (sqrt(y - 1))
-x - 6 = (sqrt(y - 1))

x = -6 +- (sqrt(y - 1))
Interchange x and y
y = -6 +- (sqrt(x - 1))
f^-1(x) = -6 +- (sqrt(x - 1))