TheCATExam
Sign in

CAT 2000 — QA Question 32

Composite FunctionsEasy
Passage / Data

Answer the following question based on the information given below.

For a real number x, let

f(x) = 1/(1 + x),                   if x is non-negative

      = 1+ x,                          if x is negative

f n(x) = f(f n – 1(x)), n = 2, 3, ....

What is the value of the product, f(2)f2(2)f3(2)f4(2)f5(2)?

Answer & solution

  • A

    13

  • B

    3

  • 118

  • D

    None of these

Solution

When x = 2, f(x) = 1/(1 + x)

f3(2)=11+2=13,f2(2)=f(f(2))=f(13)=f(13)=11+13=34

f3(2)=f(34)=11+34=47

f4(2)=f(47)=11+47=711

f5(2)=f(711)=11+711=1118

∴ f(2)f2(2)f3(2)f4(2)f5(2)=13×34×47×711×1118=118

Hence, option (c).

Hence, option (c).

CAT 2000 QA Q32: What is the value of the product, f(2)f 2 (2)f 3 (2)f 4 (2)f 5 (2)? — Solution | TheCATExam