Find the composition of the function.g(x)=sqrt(x) and g(x)=sqrt(x) find f(g(x)).
To find the composition of the functions f(g(x)), we need to substitute g(x) into f(x) and simplify the expression
To find the composition of the functions f(g(x)), we need to substitute g(x) into f(x) and simplify the expression.
Given:
g(x) = √(x)
f(x) = √(x)
Step 1: Substitute g(x) into f(x)
f(g(x)) = f(√(x))
Step 2: Simplify the expression
We substitute g(x) = √(x) into f(x) = √(x) to get:
f(g(x)) = f(√(x)) = √(√(x))
Step 3: Simplify further
To simplify the expression √(√(x)), we can rewrite it using fractional exponents:
f(g(x)) = √(√(x)) = x^(1/4)
Therefore, the composition of the functions f(g(x)) is x^(1/4).
Note: The composition f(g(x)) essentially represents the function f applied to g(x). In this case, since f(x) = √(x) and g(x) = √(x), the composition f(g(x)) simplifies to x^(1/4).
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