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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