![]() ![]() Step 2: Find the domain of the resultant function f(g(x)) and denote it by B.Step 1: Find the domain of g(x) and denote it by A.The domain of a composite function not only depends upon the resultant function but also depends on the inner function. ![]() Let us see how to find the domain and range of f(g(x)). Then the domain of f ∘ g is A and the range of f ∘ g is C. In general, if a function g : A → B and f : B → C then, f of g of x is a function such that f ∘ g : A → C. ![]() The domain of a function y = f(x) is the set of all x values where it is defined (i.e., it is the set of all inputs) and the range is the set of all y-values that the function produces (i.e., it is the set of all outputs). Here are more examples of finding f(g(x)). To find g(f(x)), substitute x = f(x) into g(x).To find f(g(x)), substitute x = g(x) into f(x).We can visualize this process using the following figure easily. Step 2: Find f(g(3)) by using g(3) as input for f(x).Let us assume that f(x) = 2x + 3 and g(x) = x 2. So for finding f(g(x)), we have to first find g(x) and then take g(x) as input of f(x) and simplify. We know that whenever we are simplifying some mathematical expression, we first operate the things that are inside the brackets. ![]()
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