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

2nd Option is correct.

Step-by-step explanation:

We need to find Even function from given functions.

Even function: Even function is a function which hold the following equation.

f(x) = f(-x) for all value of x.

Option 1).

g(x) = ( x - 1 )² + 1 = x² - 2x + 1 + 1 = x² - 2x + 2

put x = -x

g(-x) = (-x)² - 2(-x) + 2 = x² + 2x + 2

Since, g(x) ≠ g(-x)

This is not even function.

Option 2).

g(x) = 2x² + 1

put x = -x

g(-x) = 2(-x)² + 1 = 2x² + 1

Since, g(x) = g(-x)

This is even function.

Option 3).

g(x) = 4x + 2

put x = -x

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

Since, g(x) ≠ g(-x)

This is not even function.

Option 4).

g(x) = 2x

put x = -x

g(-x) = 2(-x) = 2x

Since, g(x) ≠ g(-x)

This is not even function.

Therefore, 2nd Option is correct.

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