Some hints: use the definition: f is a function iff a = b implies f(a) =...

Some hints: use the definition: f is a function iff a = b implies f(a) = f(b) and recall that in informal proofs we show an implication by assuming the if part of the implication, and then deducing the then part of the implication.

The base case will show that a = b implies f(a) = f(b) when f(x) = c₀ (a constant function). The inductive case will assume a = b implies f(a) = f(b) for degree k, and will deduce it is also true for degree k+1.

Show that every polynomial of degree n:
y = f(x) = c_nxⁿ + c_n-1x^n-1 + . . . + c₂x² + c₁x + c₀
is a function by mathematical induction on degree n.
Assume n is a nonnegative integer, all c_is are real, c_n ≠ 0, and x and y are also real.

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This is the desired proof.I hope the answer will help you.Expecting a thumbs up if you are satisfied with the work,it will help me a lot.Thank you.

Colby Messinger answered 1 year ago

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