9) Find the composition of the function.f(x) = 1/x^2 and g(x) = 1/x^3 . Find g(f(x)).
To find the composition of the functions f(x) = 1/x^2 and g(x) = 1/x^3, we need to find g(f(x)), which means plugging f(x) into g(x)
To find the composition of the functions f(x) = 1/x^2 and g(x) = 1/x^3, we need to find g(f(x)), which means plugging f(x) into g(x).
First, we need to find f(x):
f(x) = 1/x^2
Next, we substitute f(x) into g(x):
g(f(x)) = g(1/x^2)
Now, we evaluate g(1/x^2). To do this, we substitute 1/x^2 into the function g(x):
g(1/x^2) = 1/(1/x^2)^3
Simplifying further:
g(1/x^2) = 1/(1/x^6)
To divide by a fraction, flip it and multiply:
g(1/x^2) = x^6/1
The composition of the functions is g(f(x)) = x^6.
So, the final answer is: g(f(x)) = x^6.
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