I need help Its a prove math

[Viwet]

show that f:R^n R, f(x)=(x1+x2+...+xn)/n is a linear function

 

[Deleted member 4993]

show that f:R^n R, f(x)=(x1+x2+...+xn)/n is a linear function

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this problem

 

[HallsofIvy]

So basically you want to prove that this function satisfies the definition of "linear function".

What definition of "linear function" do you have?

 

[Viwet]

I have a sheet, it's a linear function condition.

 

[Deleted member 4993]

Please show us what you have tried and

exactly where you are stuck.​

 

[Steven G]

Do you not understand the definition of linearity?
You need to compute f(ax) and af(x) and say wow they really are equal.
Then you compute f(x+y) and f(x) + f(y) and again note that they are equal.
OR, you can compute f(ax+by) and af(x) + bf(y) and note that they are equal.
There are smoother ways of doing this but what I outlined above is fine for a beginning proof student.

 

[Viwet]

I get it now. Thank You very much