# CAT Practice : Functions

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Composite Functions

## Composite Function

Q.20: If $f(x) = \frac{1}{g(x)}$, 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))))))))

Choice D. f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))

## Detailed Solution

Given, $f(x) = \frac{1}{g(x)}$ =) 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.

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Functions.