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 f(g(x)), we first need to substitute g(x) into f(x):
f(g(x)) = f(1/x^3)
And then, we substitute the formula for f(x) into that expression:
f(g(x)) = 1/(1/x^3)^2
Simplifying the expression within the parentheses, we get:
f(g(x)) = 1/(1/x^6)
Now, we can simplify the expression further by multiplying the numerator and denominator by x^6:
f(g(x)) = x^6/1
Therefore, the composition of f(x) and g(x) is:
f(g(x)) = x^6
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