Respuesta :

apologiabiology
an even function can be reflected about the y axis and map onto itself
example: y=x^2

an odd function can be reflected about the origin and map onto itself
example: y=x^3


a simple test is the following

if f(x) is even then f(-x)=f(x)
if f(x) is odd then f(-x)=-f(x)


so

even function
subsitute -x for each and see if we get the same function
remember to fully expand these

g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2 is the original one

g(x)=(x-1)^2+1
g(-x)=(-x-1)^2+1
g(-x)=(1)(x+1)^2+1
g(-x)=x^2+2x+1+1
g(-x)=x^2+2x+2
not same because the original has -2x
not even


g(x)=2x^2+1
g(-x)=2(-x)^2+1
g(-x)=2x^2+1
same, it's even

g(x)=4x+2
g(-x)=4(-x)+2
g(-x)=-4x+2
not the same, not even

g(x)=2x
g(-x)=2(-x)
g(-x)=-2x
not same, not even



g(x)=2x²+1 is the even function
jayilych4real

The answer choice which is an even function from the given functions is:

  • g(x)=2x²+1

What is an Even Function?

This refers to the the equality of a function where if f of x is equal to f of −x for all the values of x.

Hence, we can see that to find the even function, we should note that it should be reflected about the y axis and map onto itself and an odd function can be reflected about the origin and map onto itself

With this, we do a simple test:

  • if f(x) is even then f(-x)=f(x)
  • if f(x) is odd then f(-x)=-f(x)

We then substitute -x for each and see if we get the same function

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

Therefore, g(x)=2x²+1 is the even function

Read more about even function here:
https://brainly.com/question/17059941

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