Simplifying the Composition of f(x) = 1/x^2 and g(x) = 1/x^3 | Finding f(g(x)) = x^6

Find the composition of the function.f(x)=1/x^2 and g(x)=1/x^3 . Find f(g(x)).

To find the composition of the functions f(x) = 1/x^2 and g(x) = 1/x^3 and find f(g(x)), we need to substitute g(x) into f(x)

To find the composition of the functions f(x) = 1/x^2 and g(x) = 1/x^3 and find f(g(x)), we need to substitute g(x) into f(x).

First, let’s find g(x):
g(x) = 1/x^3

Next, substitute g(x) into f(x):
f(g(x)) = f(1/x^3)

Now, let’s substitute 1/x^3 into f(x) using the given function f(x) = 1/x^2:
f(g(x)) = 1 / (1/x^3)^2

To simplify further, we need to simplify the expression in the denominator:
(1/x^3)^2 = 1 / (x^3)^2 = 1 / x^6

Now, substitute this back into f(g(x)):
f(g(x)) = 1 / (1 / x^6) = x^6

Therefore, f(g(x)) simplifies to x^6.

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