Write y=(2-x)^5/3 as f[g(x)], defining f(x) and g(x)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function y = (2 - x)^(5/3) has to written in the form f(g(x)) by defining arbitrary functions f(x) and g(x).

f(g(x)) = (2 - x)^(5/3)

We can use g(x) = 2 - x and f(x) = x^(5/3)

Using these functions we see that f(g(x)) = f(2 - x) = (2 - x)^(5/3)

The functions f(x) and g(x) which make f(g(x)) = (2 - x)^(5/3) are f(x) = x^(5/3) and g(x) = 2 - x

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The function y=(2-x)^5/3 has to be expressed as a compound function f(g(x)).

In the term (2 - x)^5/3, a value equal to 2 - x is raised to the power 5 and divided by 3. There are many ways that the expression y = (2 - x)^5/3 can be written as f(g(x)).

One of them is to define g(x) = 2 - x and f(x) = x^5/3

This gives: f(g(x)) = f(2 - x) = (2 - x)^5/3

Another way to do the same would be to define g(x) = (2 - x)^5 and f(x) = x/3

This gives: f(g(x)) = f((2-x)^5) and f(g(x)) = (2-x)^5/3

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