Which of the following is an even function?
g(x) = (x – 1)2 + 1
g(x) = 2x2 + 1
g(x) = 4x + 2
g(x) = 2x

To tell if it is an even function

replace all x with -x and if you get the same equaiton simplified, then it is even

g(-x)=(-x-1)^2+1
g(-x)=x^2+2x+2
original
g(x)=x^2-2x+2
not same
not even

g(-x)=2(-x)^2+1
g(-x)=2(x^2)+1
g(-x)=2x^2+1
original
g(x)=2x^2+1
same
it's even

g(-x)=4(-x)+2
g(-x)=-4x+2
original was
g(x)=4x+2
not same
not even

g(-x)=2(-x)
g(-x)=-2x
original
g(x)=2x
not same
not even

the only one that is even is
2nd one
g(x)=2x^2+1

-x-1)(-x-1