What Is The Domain Of The Composite Function G F X
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It doesn t matter if it s composite.
What is the domain of the composite function g f x. Find the domain of f. Since the notation for the composition g circ f x g f x means to first apply f to x to get f x and then to apply g to f x to get g f x a point x will be in the domain of g circ f if and only if x is in the domain of f and f x is in the domain of g. Find those inputs x in the domain of g for which g x is in the domain of f. Make sure we get the domain for f x right then also make sure that g x gets the correct domain.
When doing for example g º f x g f x. For example let f x frac x 3 x 4 and g x frac x 2 x 5. If g x x 2 x a million its area is all actual x. Even if for the composite function f g x sqrt 9 x 2 x a million 2 the area is constrained to values of x for which 3 g x 3 the decrease fee is high quality because the minimum fee of x 2 x a million is 3 4 so it is continuously more beneficial than 3.
That is exclude those inputs x from the domain of g for which g x is not in the domain of f. Given a function composition latex f left g left x right right latex determine its domain. Just like with inverse functions you need to apply domain restrictions as necessary to composite functions. The output however has to be a real number.
The number x 4 is not in the domain of f and is therefore not in the. We must get both domains right the composed function and the first function used. Find the domain of g.
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