Consider the function $f:
\mathbb R \to [1,\infty)definedbyf(x)=x^{2}+1$.
a. (i) State the definition of a surjective (onto) function.
b. (ii) Determine, with reason, whether f is surjective for the stated domain and codomain.
c. (iii) Redefine the codomain so that the same rule f(x)=x2+1 becomes surjective, and justify your choice.