So the range of f(g(x)) is found just like the range of any other function. The range of f(g(x)) doesn't depend on either the range of f or the range of g. Find f(g(x)) algebraically and find its domain.Find the domain of inner function g(x).g(f(x)) = a function obtained by replacing x with f(x) in g(x).įor example, if f(x) = x 2 and g(x) = sin x, then (i) f(g(x)) = f(sin x) = (sin x) 2 = sin 2 x whereas (ii) g(f(x)) = g(x 2) = sin x 2.f(g(x)) = a function obtained by replacing x with g(x) in f(x)."f of g of x" is written as f(g(x)) and "g of f of x" is written as g(f(x)). What is the Difference Between F of G of x and G of F of x? To find f(g(x)), we just substitute x = g(x) in the function f(x). What is the Process of Finding F of G of x? It is obtained by replacing x in f(x) with g(x). So we just compute the range of f(g(x)) using the techniques of finding the range of a function.įAQs on F of G of x What is the Definition of F of G of x?į of G of X is written as f(g(x)) and it is called a composite function. The range of f of g of x does not depend upon the inner function. So for f(g(x)) to exist at some x value, g(x) should exist first at at that x value. Step 3: Find their intersection (A ∩ B) which gives the domain of f(g(x))Įxample: Find the domain of f(g(x)) when f(x) = 2/(x - 1) and g(x) = 3/(x - 2).į(g(x)) &=f\left(\frac\) is defined at x = 2, 2 is NOT present in the domain of f(g(x)) because g(x) is NOT defined at x = 2. 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)).
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