Question

A function $f :\left[\frac{5}{2}, \infty\right) \rightarrow\left[\frac{11}{4}, \infty\right)$ defined as $f ( x )= x ^2-5 x +9$. Number of solution of the equation $f(x)=f^{-1}(x)$ will be

• A. 0
• B. 1
• C. 2
• D. $\infty$

Answer 1

Answer: (B)

$ \because f ( x )=\left( x -\frac{5}{2}\right)^2+\frac{11}{4}R$
$\therefore f \text { is one one and onto }$
$ f ( x )= f ^{-1}( x ) \text { will be same as } f ( x )= x $
$\Rightarrow x ^2-5 x +9= x \Rightarrow x ^2-6 x +9=0$
$\Rightarrow x =3$