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 first need to substitute f(x) into g(x)
To find g(f(x)), we first need to substitute f(x) into g(x).
Given f(x) = 1/x^2 and g(x) = 1/x^3, we substitute f(x) into g(x) by replacing x in g(x) with f(x):
g(f(x)) = 1/(f(x))^3
Now, substitute f(x) in place of x:
g(f(x)) = 1/(1/x^2)^3
Simplify the expression within the parentheses:
g(f(x)) = 1/(1/x^6)
To simplify further, we can rewrite 1/(1/x^6) as x^6/1:
g(f(x)) = x^6/1
Finally, simplify the expression:
g(f(x)) = x^6
Therefore, the composition g(f(x)) simplifies to x^6.
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