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 two functions, we substitute the expression for one function into the other, following the order specified
To find the composition of two functions, we substitute the expression for one function into the other, following the order specified. In this case, we want to find f(g(x)).
Given f(x) = 1/x^2 and g(x) = 1/x^3, we need to find the function f(g(x)).
To do this, we substitute g(x) into f(x):
f(g(x)) = f(1/x^3)
Now, let’s substitute 1/x^3 into f(x) by replacing all instances of x in f(x) with 1/x^3:
f(g(x)) = 1/(1/x^3)^2
Next, simplify the expression inside the brackets:
f(g(x)) = 1/(1/(x^3)^2)
Now, simplify the exponent:
f(g(x)) = 1/(1/x^6)
To divide by a fraction, we can multiply by its reciprocal:
f(g(x)) = 1 * x^6/1
Simplifying further, we get:
f(g(x)) = x^6
Therefore, the composition of the given functions f(x) = 1/x^2 and g(x) = 1/x^3 is f(g(x)) = x^6.
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