Find the composition of the function.g(x)=sqrt(x) and g(x)=sqrt(x) find f(g(x)).
x^(1/6)
To find the composition of the two functions, we can substitute g(x) into f(x), which gives us:
f(g(x)) = f(sqrt(x))
This means that we take the square root of x first (since that is what g(x) does) and then use the resulting value as the input for the function f(x).
Without knowing what f(x) is, we cannot provide a numerical answer, but we can illustrate the process with an example. Suppose that f(x) = 2x + 1, then:
f(g(x)) = f(sqrt(x)) = 2(sqrt(x)) + 1
This final expression, 2(sqrt(x)) + 1, is the composition of f(x) and g(x). Regardless of the specific functions used, the composition of f(g(x)) always results in a new function that is a combination of the two original functions.
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