1. Tardigrade
  2. Question
  3. Mathematics
  4. If f(x)= begincases2-x, x ≤ 1 2 x-x2, x>1 endcases and g is the inverse function of f, then number of solution(s) of the equation f ( x )= g ( x ) is(are)

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Q. If $f(x)=\begin{cases}2-x, & x \leq 1 \\ 2 x-x^2, & x>1\end{cases}$ and $g$ is the inverse function of $f$, then number of solution(s) of the equation $f ( x )= g ( x )$ is(are)

Relations and Functions - Part 2

Solution:

$f(x)=\begin{cases}2-x, & x \leq 1 \\ 2 x-x^2, & x>1\end{cases}$
image
Clearly, $f ( x )$ and $f ^{-1}( x )$ meet each other at $(0,2),(1,1),(2,0)$.