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\(If $f(x) = \begin{cases} 2x-5 &\quad \text{if } x \ge 3, \\ -x + 5 &\quad \text{if } x < 3, \end{cases}$, then for how many values of $x$ is $f(f(x)) = 3$?\)

 Aug 19, 2022
 #1
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f(f(x) )  =   2(-x + 5) - 5  =   -2x + 5

f(f(x))  =  3

-2x + 5 =  3

-2x  =  -2

x  = 1

 

or

 

f(f(x))   = -(2x - 5) + 5   =  -2x + 10

f(f(x)) =  3

-2x + 10 =  3

-2x  =  -7

x = 7/2  = 3.5

 

cool cool cool

 Aug 19, 2022

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