Consider the function defined by .

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Consider the function

f:\mathbb{R}\to[1,\infty)

defined by

f(x)=x^2+1

. (i) State the definition of a surjective (onto) function. (ii) Determine, with reason, whether

f

is surjective for the stated domain and codomain. (iii) Redefine the codomain so that the same rule

f(x)=x^2+1

becomes surjective, and justify your choice.