Question

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

Answer 1

c. g(x)=4x+2. I hope it will help u

Answer 2

Even function should be symmetric around Y-axis. Which means the function has to be f(-x) = f(x)

Let us check the functions one by one whether they satisfy the above property of an even function,

A.

g(-x) = [(-x)-1]2 + 1

            = (-x-1)2 + 1

            = -(x+1)2 +1

            $\neq$ g(x)

B.

g(-x) = 2x2 +1

        = 2x2 +1

        = g(x)           ; (function wont change if we substitute x or -x for the                       equation)

C.

g(-x) = 4(-x) + 2

       = -4x + 2

       $\neq$ g(x)

D.

g(-x) = 2(-x)

       $\neq$ g(x)

So the answer should be "B"