Answer:
{52}
Step-by-step explanation:
The calculator function appears to be ...
f(x) = {3x -1, x odd; x/2 +1, x not divisible by 4; x/4, x divisible by 4}
The inverse of the first function is ...
x = 3y -1
(x+1)/3 = y . . . . (y must be odd)
For x = 13, this is 14/3, which is not an integer.
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The inverse of the second function is ...
x = y/2+1
2(x-1) = y . . . . (y must <em>not</em> be divisible by 4)
For x = 13, this is 2·12 = 24, which is divisible by 4, so 24 is not the input value.
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The inverse of the third function is ...
x = y/4
4x = y . . . . (y must be, and is, divisible by 4)
For x = 13, this is 4·13 = 52.
The only possible input value for an output of 13 is 52.
