Let f(x) = a_0 + a_1x + \cdots + a_nx^nf(x)=a 0 +a 1 x+⋯+a...

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Let f(x) = a_0 + a_1x + \cdots + a_nx^nf(x)=a 0 +a 1 x+⋯+a...

Let f(x) = a_0 + a_1x + \cdots + a_nx^nf(x)=a 0 +a 1 x+⋯+a n x n be a polynomial of degree less than or equal to nn, and let \{x_0,x_1,\ldots,x_n\}{x 0 ,x 1 ,…,x n } be distinct points. What is the value of f[x_0,x_1,\ldots,x_n]f[x 0 ,x 1 ,…,x n ]? Explain.

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Answer 1

Answer #1

f(x) is a polynomial in one variable x so it takes one value at a time. If x_0, x₁,.....x_n are distinct points then f gives one value for each points which are f(x₀), f(x₁).....,f(x_n). So f[x₀,x₁,.....x_n] does not make sense.

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Answer 2

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