Respuesta :

Answer:

The second function represents an even function; [tex]g(x)=2x^{2} +1[/tex]

Step-by-step explanation:

A function f(x) is said to be even if f(x) = f(-x). All we need to do is replace x with -x in each equation, simplify it and assess whether the equation remains unchanged. If  the equation is identical to the original one then it is said to be even. Another good example of an even function is the cosine function. Moreover, even functions have y-axis symmetry

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Answer:

Choice B is correct answer.

Step-by-step explanation:

We have given four functions.

We have to choose the even function.

A function is even when

       f(x) = f(-x)

A.   g(x) = (x-1)²+1

   g(-x) = (-x-1)²+1

   g(-x) ≠ g(x)

B.  g(x) = 2x²+1

 g(-x) = 2(-x)²+1

   g(-x) =  2x²+1

hence, g(x) =  g(-x)

C.   g(x) = 4x+2

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

g(-x) =  -4x+2

hence,  g(-x) ≠ g(x)

D.    g(x) =2x

  g(-x) = 2(-x)

  g(-x) = -2x

hence,  g(-x) ≠ g(x)

Choice B is correct answer.

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