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The input to a function need not be a number, it can be any well defined object. For example, a function might associate the letter A with the number 1, the letter B with the number 2, and so on.

If the inputs and outputs are numbers, then the most obvious examples are the polynomials.

f(x) = x + 1 is a simple example, a function that adds one to the input.

f(1) = 1 + 1 = 2, f(2) = 2 + 1 = 3.

Also, g(x) = 2x is a function that doubles the input.

g(3) = 6, g(4) = 8.

Another example is h(x) = 2x + 1. This doubles the output, and adds 1. The result is that h(1) = 2*1 + 1 = 3, h(2) = 2*2 + 1 = 5.

i(x) = x is another function that does nothing to x. So i(1) = 1, i(2) = 2.

f(x)=x^3+14x^2+63x+90 x=-6 Finding root using the Factor Theorem

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Q: What is the set of all possible outputs values of a function?
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