The Composition of Functions f(x) and g(x) for Mathematical Analysis

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

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

Given:
f(x) = x^(1/3)
g(x) = √x

To find g(f(x)), we substitute f(x) into g(x):
g(f(x)) = g(x^(1/3))

We substitute x^(1/3) into g(x):
g(f(x)) = √(x^(1/3))

To simplify this further, we can apply a property of radicals: √(a^b) = (a^(b/2))
Therefore, we can rewrite the expression as:
g(f(x)) = (x^(1/3))^(1/2)

Now, we can simplify the exponent of x:
g(f(x)) = x^((1/3)*(1/2))

Multiplying the exponents, we have:
g(f(x)) = x^(1/6)

So, the composition of the functions f(x) = x^(1/3) and g(x) = √x is g(f(x)) = x^(1/6).

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