Question

What is the inverse of f(x)=x^2-2x, x is greater than or equal to 1? Simplify the inverse and state the domain of f^-1?? and the inverse were its less than or equal to 1.

Answer 1

@csmith3455

Answer 2

To find the inverse of f(x),

1. set y = f(x),
2. swap variables x and y.
3. solve for y by completing the square
4. Replace y with \(f−1(x)\)

1. \(y=x2−2x\)
2. \(x=y2−2y\)
3. \(x+1=y2−2y+1\)
\(x+1=(y−1)^2\)
\(±\sqrt{x+1}=y−1\)
\(±\sqrt{x+1}+1=y\)

4. The inverse is not a function

Technically, the inverse of f(x) is not a function so we should not use the notation f−1(x)