Mathematics

Problem

Answer the following with respect to the concept of surjectivity of functions. a. Part 1: (i) Define a surjective (onto) function. b. Part 2: (ii) Let

f: \mathbb{R} \to [0,\,\infty)

be given by

f(x)=x^{2}

. Determine, with justification, whether

f

is surjective. c. Part 3: (iii) If the same rule

f(x)=x^{2}

is declared with codomain

\mathbb{R}

instead of

[0,\,\infty)

, state with reason whether the function is surjective in this case.

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