Find the composition of the function.f(x)=1/x^2 and g(x)=1/x^3 . Find g(f(x)).
x^6
To find g(f(x)), we need to first find the composition of the two functions f and g.
Let’s start by finding f(g(x)):
f(g(x)) = f(1/x^3) = 1/(1/x^3)^2 = 1/x^6
Now, to find g(f(x)) we just need to substitute f(x) in place of x in the function g:
g(f(x)) = g(1/x^2) = 1/(1/x^2)^3 = 1/x^6
So, g(f(x)) = f(g(x)) = 1/x^6.
Therefore, the composition of the given functions is g(f(x)) = f(g(x)) = 1/x^6.
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