While g(x) has domain all the real numbers and range R +. The domain of both the functions are real numbers, so there is no need to modify the domain for the first function in any case.į(x) has domain as all real numbers and range. Find out the values of f(g(x) and g(f(x)). Question 1: For the given functions f(x) = e x and g(x) = x 2 + 1. Let’s see some problems with these concepts. The range of the composed function is either the same as the range of the second function, or else lies inside it. Domain of g(x) should be modified such that the range of g(x) lies inside the domain of f(x).ĭomain of the composed function is either same as the domain of the first function or else lies inside it.In the case of f(g(x)), the range of g(x) must lie inside the domain of f(x).In such cases following things should be kept in mind: For other pairs, the domains can be modified.
So, the range of f(x) should lie within the domain of g(x).įor some pair of functions, it is not possible to make a composite function out of them. So, in the case, f(g(x)) we need to make sure that log(x) does not give negative values as the outputs. In this case, the domain of f(x) is positive real numbers. In another case, let’s say f(x) = √x and g(x) = log(x). So, there are certain things that should be kept in mind while deciding on composing the function. If we try to compose f(g(x)), it is not possible as the logarithmic function cannot take negative input values, so f(g(x)) is not possible. It is not possible to compose any two functions, some functions cannot be composed together for example, let’s say f(x) = ln(x) and g(x) = -x 2. Range: Set of corresponding outputs by the function.ĭomain and Range of composition of functions While deciding which values are valid as input, we need to keep in mind that on any of the inputs, the function should not become undefined or give imaginary numbers in the output.ĭomain: Set of all possible input to the function. There are certain values that can be given as input to the function and function gives outputs correspondingly.
This violates the definition of a function. Now let’s plot these values on graph.Ī function cannot have one input value giving two outputs. The graph of the function can be plotted by taking different input values and finding the function output over them. It seems that any number can be picked as an argument, but that is not the case. When the argument is chosen as x = 2, the function gives an output of 5. The number “x” is called the argument of the function.
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