How do you find f^-1(x)f−1(x) given f(x)=(x+2)^2+6f(x)=(x+2)2+6?
1 Answer
Explanation:
Given:
f(x) = (x+2)^2+6f(x)=(x+2)2+6
We can attempt to derive an inverse function as follows:
Let:
y = f(x) = (x+2)^2+6y=f(x)=(x+2)2+6
Subtract
y-6 = (x+2)^2y−6=(x+2)2
Take the square root of both sides, allowing for both possible signs:
+-sqrt(y-6) = x+2±√y−6=x+2
Transpose and subtract
x = -2+-sqrt(y-6)x=−2±√y−6
Note that for any value of
Since
Alternatively, we can define an inverse image function
F^(-1)(y) = { -2+sqrt(y-6), -2-sqrt(y-6) }
