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Question 25

The program below contains variables whose values are defined with lambda functions.

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2
3
4
f1 = (lambda x: x * x)
f2 = (lambda x: int(x ** 3))
f3 = (lambda x: x // 2)
f4 = (lambda x: x * 4)

If num = 5, which of the following produces the smallest value? [3 marks]

  • f4(f3(f1(f2(num))))
  • f4(f1(f2(f3(num))))
  • f3(f2(f1(f4(num))))
  • f2(f3(f2(f3(num))))
  • f1(f4(f2(f3(num))))
Solution 
f4(f3(f1(f2(num))))
= f4(f3(f1(int(5**3)))) = f4(f3(f1(125)))
= f4(f3(125 * 125)) = f4(f3(15625))
= f4(15625 // 2) = f4(7812)
= 31248

f4(f1(f2(f3(num))))
= f4(f1(f2(5 // 2))) = f4(f1(f2(2)))
= f4(f1(int(2 ** 3))) = f4(f1(8))
= f4(8 * 8) = f4(64)
= 64 * 4 = 256

f3(f2(f1(f4(num))))
= f3(f2(f1(5 * 4))) = f3(f2(f1(20)))
= f3(f2(20 * 20)) = f3(f2(400))
= f3(int(400**3)) = f3(64000000)
= 64000000 // 2 = 32000000

f2(f3(f2(f3(num))))
= f2(f3(f2(5 // 2))) = f2(f3(f2(2)))
= f2(f3(int(2**3))) = f2(f3(8))
= f2(8 // 2) = f2(4)
= int(4**3) = 64

f1(f4(f2(f3(num))))
= f1(f4(f2(5 // 2))) = f1(f4(f2(2)))
= f1(f4(int(2**3))) = f1(f4(8))
= f1(8 * 4) = f1(32)
= 32 * 32 = 1024

Hence, f2(f3(f2(f3(num)))) yields the smallest result out of all the given options.

Answer 
f2(f3(f2(f3(num))))