Answer to Question #329764 in Calculus for Abdul Wahid Ibrahi

Question

Let f: R->R be defined by f(x)=x²+2 where R is the set of real numbers

(i) find the domain and range of f

(ii) is f one-to-one or onto ?

Answer 1

$i:\\Dom\left( f \right) =\mathbb{R} -\,\,defined\,\,for\,\,all\,\,x\\Range\left( f \right) =\left\{ x^2+2,x\in \mathbb{R} \right\} =\left\{ t\geqslant 2 \right\} =\left[ 2,+\infty \right) \\ii:\\f\left( 1 \right) =3\\f\left( -1 \right) =3\\Not\,\,one-to-one\\f\left( x \right) =0\Rightarrow x^2+2=0\Rightarrow x^2=-2\Rightarrow x\in \emptyset \\Not\,\,onto$