Simplifying the Composition of Functions | g(f(x)) = sqrt(x)

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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