Question

Find the inverse of the quadratic function f. $f\left(x\right)=x^2-2x,x\ge 1$

• A.
• B.
• C. x²-4
• D.
• E.

Answer 1

The correct option is D

Using the technique for inverse function at x=1, f(x) = -1

Replace x by f(x) in the answer options and

Look for an answer options where x= -1, $\&$ f(x)=1

Answer is option (d)

2nd method: - Let y $=x^2-2x$

$x^2-2x-y=0$

Let $y=x^2-2x$

$x=\frac{2\pm \sqrt{4+4y}}{2}$

$x=1\pm \sqrt{1+y}$

Replace y by x,

$f(x{)}^{-1}=1\pm \sqrt{1+x}$