Question

Are x+x^2 and u+u^2 the same function? If x and u are for all real numbers? A- these are the same function B- If x and u are two different numbers, the functions are different C- there is not enough information to answer this question.

Answer 1

(a) These are the same function

Explanation:

Given

`x + x^2` and
`u + u^2`

Required

Are they the same?

Yes, they are the same function and this is proved below.

`x + x^2`

Represent as a function:

`f(x) = x + x^2`

`u + u^2`

Represent as a function

`f(u) = u + u^2`

Let x = u

Substitute u for x in
`f(x) = x + x^2`

`f(u) = u + u^2`

This implies that:

`f(x) = f(u)`

`x + x^2 =u + u^2`

PS: The information that x and u are real numbers are for all real numbers; So, we can not assume that x and u are different numbers

Hence:

(b) and (c) are wrong