If f(x)= begincases2-x, x ≤ 1 2 x-x2, x1 endcases and g is the inverse function of f, then number of solution(s) of the equation f ( x )= g ( x ) is(are)

Question

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) (A) 0 (B) 1 (C) 3 (D) infinite

Tardigrade Admin · Accepted Answer

f(x)= begincases2-x, x ≤ 1 2 x-x2, x>1 endcases <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/ac82240284832c650ce3a1b6f7466c74-.png" /> Clearly, f ( x ) and f -1( x ) meet each other at (0,2),(1,1),(2,0).

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

0

1

3

infinite

$f (x) = {2 - x, 2 x - x^{2}, x \leq 1 x > 1$

Clearly, $f (x)$ and $f^{- 1} (x)$ meet each other at $(0, 2), (1, 1), (2, 0)$ .

Q. If f(x)={2−x,2x−x2,​x≤1x>1​ and g is the inverse function of f, then number of solution(s) of the equation f(x)=g(x) is(are)

0

1

3

infinite

f(x)={2−x,2x−x2,​x≤1x>1​ Clearly, f(x) and f−1(x) meet each other at (0,2),(1,1),(2,0).

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

$f (x) = {2 - x, 2 x - x^{2}, x \leq 1 x > 1$

Clearly, $f (x)$ and $f^{- 1} (x)$ meet each other at $(0, 2), (1, 1), (2, 0)$ .