Answer:
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.
