[tex]f(x)\ is\ an\ even\ function\ if\ f(-x)=f(x)\\--------------------\\\\g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2\\g(-x)=(-x-1)^2+1=x^2+2x+1+1=x^2+2x+2\\g(-x)\neq g(x)\ it's\ not\ an\ even\ function[/tex]
[tex]g(x)=2x^2+1\\g(-x)=2(-x)^2+1=2x^2+1\\g(-x)=g(x)\ it's\ an\ even\ function\\\\\\g(x)=4x+2\\g(-x)=4(-x)+2=-4x+2\\g(-x)\neq g(x)\ it's\ not\ an\ even\ function\\\\\\g(x)=2x\\g(-x)=2(-x)=-2x\\g(-x)\neq g(x)\ it's\ not\ an\ even\ function[/tex]
