How to Find the Composition of Functions: Step-by-Step Guide with Examples

Find the composition of the function.f(x)=x^1/3 and g(x)=x Find g(f(x)).

To find the composition of the functions, we substitute the expression for the inner function f(x) into the outer function g(x)

To find the composition of the functions, we substitute the expression for the inner function f(x) into the outer function g(x).

Given f(x) = x^(1/3) and g(x) = x, we need to find g(f(x)).

To do this, we substitute f(x) into g(x):

g(f(x)) = g(x^(1/3))

Now, since g(x) is simply x, we can replace x in the expression g(x^(1/3)) with f(x) = x^(1/3):

g(f(x)) = f(x)^(1/3)

Therefore, the composition of the functions g(f(x)) is f(x) raised to the power of 1/3.

In other words, g(f(x)) = (x^(1/3))^(1/3).

Simplifying this expression, we can multiply the exponents:

g(f(x)) = x^((1/3) * (1/3))

Multiplying the exponents gives:

g(f(x)) = x^(1/9)

So, the composition of the functions g(f(x)) is x raised to the power of 1/9.

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