Question

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

Answer 1

even means g(-x)=g(x)
replace x with -x and see if it simplifies to original functin


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

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

we are done


answer is 2nd one

Answer 2

2nd Option is correct.

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.