Question 6.

Let r be a real number and $f(x)=\left\{\begin{array}{cl}2 x-rㅤ\text { if } x \geq r \\ rㅤ ㅤ \text { if } x\lt r\end{array}\right.$ Then, the equation f(x) = f(f(x)) holds for all real values of x where

A

x ≤ r

B

x ≥ r

C

x > r

D

x ≠ r

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Text Explanation

When x< r

f(x) = r

f(x) = f(f(x))

r = f(r)

r= 2r-r

r=r

When x>=r

f(x) = 2x-r

f(x) = f(f(x))

2x-r = f(2x-r)

2x-r = 2(2x-r) - r

2x-r = 4x-3r

or, x=r

Therefore x<= r

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