Question

Let $f\left(x\right)=x^2-x+1$, $x\ge \frac{1}{2}$ then the solution of the equation $f^{-1}\left(x\right)=x$ is

• A. x = 1
• B. x = 2
• C. $x=\frac{1}{2}$
• D. None of these

Answer 1

The correct option is A x = 1

Here, $f^{-1}\left(x\right)=f\left(x\right)=x$
$\Rightarrow x^2-x+1=x$
Or $x^2-2x+1=0$
$x=1$