8) 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 f(g(x)), we need to substitute g(x) into f(x)
To find the composition of f(g(x)), we need to substitute g(x) into f(x).
First, let’s find g(x) by substituting x into the function g(x) = 1/x^3:
g(x) = 1/x^3
Next, let’s substitute g(x) into f(x) by replacing x with g(x):
f(g(x)) = f(1/x^3)
Now, let’s find f(1/x^3) by substituting 1/x^3 into the function f(x) = 1/x^2:
f(g(x)) = f(1/x^3) = 1/(1/x^3)^2
To simplify this, we need to square the denominator:
f(g(x)) = f(1/x^3) = 1/(1/x^6)
Now, let’s simplify further by multiplying the numerator and denominator by the reciprocal of the denominator:
f(g(x)) = f(1/x^3) = (x^6)/1
Finally, we can simplify further to get the composition of f(g(x)):
f(g(x)) = f(1/x^3) = x^6
Therefore, the composition of the functions f(x) = 1/x^2 and g(x) = 1/x^3 is f(g(x)) = x^6.
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