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 ?
i:Dom(f)=R− defined for all xRange(f)={x2+2,x∈R}={t⩾2}=[2,+∞)ii:f(1)=3f(−1)=3Not one−to−onef(x)=0⇒x2+2=0⇒x2=−2⇒x∈∅Not ontoi:\\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\,\,ontoi:Dom(f)=R−definedforallxRange(f)={x2+2,x∈R}={t⩾2}=[2,+∞)ii:f(1)=3f(−1)=3Notone−to−onef(x)=0⇒x2+2=0⇒x2=−2⇒x∈∅Notonto
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