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 two functions, we substitute the expression of one function into the other and simplify
To find the composition of two functions, we substitute the expression of one function into the other and simplify. In this case, we want to find f(g(x)), so we will substitute g(x) into f(x).
Given f(x) = 1/x^2 and g(x) = 1/x^3.
Substituting g(x) into f(x), we have f(g(x)) = f(1/x^3).
Now, replace x in f(x) with 1/x^3:
f(g(x)) = 1/(1/x^3)^2.
Simplifying inside the parentheses:
1/(1/x^3)^2 = 1/(1/x^6) = 1 * x^6/1 = 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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