Find the composition of the function.f(x)=x^1/2 and g(x)=1x Find g(f(x)).
To find the composition of the functions f(x) and g(x), denoted as g(f(x)), we need to substitute the expression for f(x) into g(x) and simplify
To find the composition of the functions f(x) and g(x), denoted as g(f(x)), we need to substitute the expression for f(x) into g(x) and simplify.
Given:
f(x) = x^(1/2)
g(x) = 1x
To find g(f(x)), we substitute f(x) into g(x):
g(f(x)) = g(x^(1/2))
Now, let’s simplify the expression:
First, we evaluate f(x) = x^(1/2):
f(x) = x^(1/2) = sqrt(x)
Now, substitute sqrt(x) into g(x):
g(f(x)) = g(sqrt(x))
Finally, simplify g(sqrt(x)):
g(sqrt(x)) = 1(sqrt(x)) = sqrt(x)
Therefore, the composition of the functions g(x) and f(x) is g(f(x)) = sqrt(x).
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