Tuesday, July 17, 2012

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

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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