Finding the Composition of Functions: 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) and g(x), we need to substitute g(x) into f(x)

To find the composition of the functions f(x) and g(x), we need to substitute g(x) into f(x).

Given f(x) = 1/x^2 and g(x) = 1/x^3, we need to find f(g(x)).

To find f(g(x)), we substitute g(x) into f(x):

f(g(x)) = f(1/x^3)

Now, substitute 1/x^3 into f(x):

f(1/x^3) = 1/(1/x^3)^2

To simplify this further, we can rewrite the denominator:

1/(1/x^3)^2 = 1/(1/x^6)

To divide by a fraction, we multiply by its reciprocal:

1/(1/x^6) = x^6/1

Simplifying this expression, we get:

f(g(x)) = x^6

Therefore, the composition of the functions f(x) = 1/x^2 and g(x) = 1/x^3 is f(g(x)) = x^6.

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