# CAT Practice : Functions

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Substitute x = 3 or x = -3 as appropriate for the function of a function and get the values.

## Function of a function

Q.11: x is a real number such that f(x) = 1/x when x > 0 and f(x) = 1/(x + 1) otherwise. Also fn(x) = f(fn - 1 (x)). What is f(3) + f2(-3) + f3(3) + f4(-3)?
1. -2/3
2. 14/3
3. 0
4. 3

Choice B. 4/3

## Detailed Solution

f(x) = 1/x when x > 0; f(x) = 1/(x + 1) otherwise
f(3) = 1/3
f(-3) = -1/2
f2(3) = f(f(3) = f(1/3) = 3
f2(-3) = f(f(-3) = f(-1/2) = 1/(-1/2 + 1) = 2

f(3) + f2(-3) + f3(3) + f4(-3)
= = 1/3 + f(f1(-3)) + f(f2(3)) + f(f3(-3))
= = 1/3 + f(-1/2) + f(3) + f(f(f2(-3)))
= 1/3 + 2 + 1/3 + f(f(2))
= 8/3 + f(1/2)
= 8/3 + 2
= 14/3

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Functions.