How to Find the Composition of Functions | Step-by-Step Guide and Example with Simplification

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) and g(x), we need to substitute f(x) into the function g(x)

To find the composition of the functions f(x) and g(x), we need to substitute f(x) into the function g(x).

First, we 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 find g(y) where y = 1/x^2:
g(y) = 1/y^3

Substituting y into the function:
g(f(x)) = g(1/x^2) = 1/(1/x^2)^3

Simplifying further:
g(f(x)) = 1/(1/x^6)

To simplify the expression inside the parentheses, we can multiply the numerator and denominator by x^6 to eliminate the negative exponent:
g(f(x)) = 1/(1/x^6) = x^6/1 = x^6

Therefore, the composition function g(f(x)) is equal to x^6.

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