Let R[x] be the set of all polynomials with real coefficients. In other words, x] = {anx" + an-1x"-1 + ..· + a‚x + aolan, ...,ao E R} Consider the following function with domain and co-domain R[x]. : R[x] – R[x] by the rule (f(x)) = f'(x) This function, known as the "differential operator," is used and studied in calculus. The input of the function is a polynomial and the output is the derivative of that polynomial. a) What is the image of the polynomial 3x? – 10x + 5? b) Is the function one-to-one? Prove or disprove. c) Is the function onto? Prove or disprove.

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