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 the composition of the functions f(x) and g(x) and evaluate g(f(x)), we need to substitute f(x) into g(x) wherever we see x in the equation of g(x).
First, we find f(x):
f(x) = 1/x^2
Next, we find g(f(x)):
g(f(x)) = g(1/x^2)
Now we substitute 1/x^2 for x in the equation for g(x):
g(1/x^2) = 1/(1/x^2)^3
Simplifying the expression inside the parentheses:
1/(1/x^2)^3 = 1/1/x^6
Using the rule of fractional exponents:
1/1/x^6 = x^6
Therefore, the composition of the functions f(x) and g(x) is:
g(f(x)) = x^6
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