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# If $A=\{x:x\in R\:\:and\:\:x\geq \large\frac{1}{2}\}$ and $B=\{x:x\in R\:\:and\:\:x\geq\large\frac{3}{4}\}$ and $f:A\rightarrow B$ is defined as $f(x)=x^2-x+1$ so that $f(x)=f^{-1}(x)$ then the solution set of $x$ is ?

(A) $\{1\}$

(B) $\{2\}$

(C) $\{\large\frac{1}{2}\}$

(D) No Solution

If $f^{-1}(x)=f(x)$, then $fof=x$ and $f^{-1}(x)=x$
$\Rightarrow\:x^2-x+1=x$
$\Rightarrow\:(x-1)^2=0$ or $x=1$