Question

f(x) = sqrt x + sqrt (4 - x) , 0 <= x <= 2
Find the value of x such that ff^-1(x) = f^-1f(x).

Answer 1

I guess all values of x satisfy this. since the function is one to one in the given interval

Answer 2

all values of x satisfy that equation.....thats how the inverse is defined

Answer 3

*if the inverse exists

Answer 4

f(x) is 1-1 on [0,2] so the inverse do exist.

so f(f^-1(x)) = f^-1(f(x)) = x in [0,2]

Answer 5

This function is strictly increasing on the interval given. So it is one to one. SO it has an inverse.

Answer 6

But the answer given is 2 and not a range...

Answer 7

I managed to solve it. My answer is this.
Domain of f^-1 = Range of f = [2 , 2 sqrt 2]
Domain of ff^-1 = Domain of f^-1 = [2 , 2 sqrt 2]
Domain of f^-1f = Domain of f = [0 , 2]
The answer is the intersection of the two domains, which is x = 2.