Find the composition of the function.f(x)=1/x^2 and g(x)=1/x^3 . Find g(f(x)).
To find g(f(x)), we need to substitute the function f(x) into g(x)
To find g(f(x)), we need to substitute the function f(x) into g(x).
Given:
f(x) = 1/x^2
g(x) = 1/x^3
First, we find f(x) and then substitute it into g(x):
f(x) = 1/x^2
Substituting f(x) into g(x):
g(f(x)) = g(1/x^2)
Now, substitute 1/x^2 into g(x):
g(f(x)) = 1/(1/x^2)^3
Simplifying further:
g(f(x)) = 1/(1/x^6)
Using the power of a quotient rule, x^(-a) = 1/x^a:
g(f(x)) = x^6/1
Simplifying:
g(f(x)) = x^6
So, the composition of g(f(x)) is x^6.
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