How do you write y=2(x3)55(x3)2+0.5(x3)+11 as a composition of two simpler functions?

1 Answer
Oct 27, 2015

f(x)=2x55x2+0.5x+11,

g(x)=x3

Explanation:

There is no algorithm to solve this exercise, you only can see that your expression resembles a polynomial, since it is the sum of the powers of a certain quantity (namely x3), with some coefficient. So, a polynomial described by words would be "pick a constant, add a certain quantity multiplied by some coefficient, then add the square of that quantity multiplied by some coefficient, and so on". And it is exactly what's happening here: you have 11, then you have the first power of x3 multiplied by 0.5, then you have the second power of x3 multiplied by 5, and finally you have the fifth power of x3 multiplied by 2.

So, you have a function f which plays the role of the polynomial:

f(x)=2x55x2+0.5x+11,

and you're evaluating it at g(x)=x3 (what I called the "quantity" above).

So, the result is the combination f(g(x))