# how to find composite function f(f(x)) , where f(x) is any peice wise defined function.please explain..

105 Points
13 years ago

Dear Amit,

A composite function is one in which the output of one function becomes the input for another. The notation f(g(x)), read "f of g of x", where f and g are both functions of x.
In f(g(x)), the g(x) function is substituted for x in the f(x) function. Similarly, in g(f(x)), the f(x) function is substituted for x in the g(x) function.

IN our case f(x) is substituted in f(x)

Finding the domain of a composite function consists of two steps:

Step 1. Find the domain of the "inside" (input) function. If there are any restrictions on the domain, keep them.
Step 2. Construct the composite function. Find the domain of this new function. If there are restrictions on this domain, add them to the restrictions from Step 1. If there is an overlap, use the more restrictive domain (or the intersection of the domains). The composite may also result in a domain unrelated to the domains of the original functions

All the best.

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