Let $A = \{x∈R: x≥1/2\}$ and $B=\{x∈R:x≥3/4\}$. If f: A → B is defined as $f(x) = x^2-x+1$, then the solution set of the equation $f(x) = f^{−1}(x)$ is

{1}

The correct answer is Option (1) → {1}

Clearly, f: A → B is a bijection. This fact can also be observed from the graph of f(x) as it represents an arc of the parabola $y = x^2 -x + 1$ lying on the right side of the vertex (1/2, 3/4).

We know that the curves $y = f (x)$ and $y = f^{-1} (x)$ are mirror images of each other in the line mirror $y = x$. This means that the two curves intersect at points lying on the line $y = x$.

$∴f(x) = f^{-1}(x)$

$⇒f(x) = x = x^2-x+1=x⇒ (x-1)^2=0⇒ x=1$

Hence, the solution set of the equation $f(x) = f^{-1} (x)$ is {1}.