Question

Which of the following is an even function?

Answer 1

$f(x)\ is\ an\ even\ function\ if\ f(-x)=f(x)\\--------------------\\\\g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2\\g(-x)=(-x-1)^2+1=x^2+2x+1+1=x^2+2x+2\\g(-x)\neq g(x)\ it's\ not\ an\ even\ function$

$g(x)=2x^2+1\\g(-x)=2(-x)^2+1=2x^2+1\\g(-x)=g(x)\ it's\ an\ even\ function\\\\\\g(x)=4x+2\\g(-x)=4(-x)+2=-4x+2\\g(-x)\neq g(x)\ it's\ not\ an\ even\ function\\\\\\g(x)=2x\\g(-x)=2(-x)=-2x\\g(-x)\neq g(x)\ it's\ not\ an\ even\ function$

Answer 2

Hello,

A function f(x) is even if f(-x)=f(x).

A: (x-1)²+1≠((-x)-1)²+1

B:2x²+1=2(-x)²+1 is even

C:4x+2≠4*(-x)+2

D:2x≠2*(-x)

Answer B