Find the composition of the function.f(x)=1/x^2 and g(x)=1/x^3 . Find f(g(x)).
x^6
To find the composition of f(x) and g(x):
Step 1: Substitute g(x) into f(x), which means replace x in f(x) with g(x).
f(g(x)) = 1/(g(x))^2
Step 2: Substitute g(x) into the expression for g(x).
g(x) = 1/x^3
f(g(x)) = 1/(g(x))^2 = 1/[(1/x^3)^2] = 1/(1/x^6) = x^6
Therefore, the composition of f(x) and g(x) is f(g(x)) = x^6.
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