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The function f(x) is defined for 1 \le x \le 5 as follows:

f(x) = 2x + 8 if 1 \le x \le 2

f(x) = 13 - 5x if 2 < x \le 3

f(x) = 20 - 14x if 3 < x \le 4

f(x) = 40 + 5x if 4 < x \le 5

 

Find all real numbers x such that f(x) = x.  If you find more than one answer, list them all, separated by commas.

 Feb 8, 2024
 #1
avatar+129830 
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2x + 8  = x

x = -8          No, x not in the domain  of (1,2)

 

13 - 5x  = x

13 = 6x

x =13/6     Yes, x  in the domain  of (2,3)

 

20 -14x  = x

20  = 15x

x = 20/15  = 4/3   No, x not in the domain (3 ,4)

 

40 + 5x  = x

40 = -4x

x = 40/-4  = -10    No, x not in the domain (4,5)

 

Answer    x   =13/6

 

cool cool cool

 Feb 8, 2024

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