Find the composition of the function.f(x)=x^1/2 and g(x)=1x Find g(f(x)).
x^(-1/2)
To find g(f(x)), we need to substitute the expression for f(x) into the expression for g(x). So first, we need to find f(x):
f(x) = x^(1/2)
Now, we substitute out f(x) in g(x):
g(f(x)) = g(x^(1/2))
Next, we need to find g(x^(1/2)). From the expression g(x) = 1x, we can see that g(x) just gives us back x. So if we input x^(1/2) into g(x), we get:
g(x^(1/2)) = 1x^(1/2)
Therefore, g(f(x)) = g(x^(1/2)) = 1x^(1/2) = √x.
So the composition of the functions f(x) and g(x) is g(f(x)) = √x.
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