CAT Practice : Functions

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Composite Functions

Composite Function

    Q.20: If , then which of the following is correct?
    1. f(f(g(g(f(x))))) = g(f(g(g(g(x)))))
    2. f(f(f(g(g(g(f(g(x)))))))) = g(g(g(g(f(g(f(f(x))))))))
    3. f(f(g(f(x)))) = g(g(f(g(x))))
    4. f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))


  • Correct Answer
    Choice D. f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))

Detailed Solution

Given, =) f(x).g(x) = 1 which implies that f(x) and g(x) are essentially inverse of one another. So, one just have to look for an option which has equal number of fs and gs on both side of the equation.
Answer choice (D).

Correct Answer: f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))

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