Question

Which of the following is an even function?

g(x) = (x - 1)2 + 1
Og(x) = 2x2 + 1
O g(x) = 4x + 2
g(x) = 2x

Answer 1

B

Explanation:

Just took test on edge

Answer 2

Answer: Second Option

`g(x) = 2x^2 + 1`

Explanation:

By definition, a function f(x) is an even function if:

`f (-x) = f (x)`

This means that each input value x and its negative -x are assigned the same output value y.

To verify which of the functions is even, you must test
`f(-x) = f(x)` for each of them

First option

`g(x) = (x - 1)^2 + 1`

`g(-x) = (-x -1)^2 +1\\\\g(-x) = ((-1)(x+1))^2 +1\\\\g(-x) = (-1)^2(x+1)^2 +1\\\\g(-x) = (x+1)^2 +1\\eq g(x)`

Second option

`g(x) = 2x^2 + 1`

`g(-x) = 2(-x)^2 + 1`

`g(-x) = 2x^2 + 1=g(x)`

Third option

`g(x) = 4x + 2`

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

`g(-x) = -4x + 2\\eq g(x)`

Fourth option

`g(x) = 2^x`

`g(-x) = 2^(-x)`

`g(-x) = (1)/(2^x)\\eq g(x)`