Change of Variables: Understanding Homework Statement

[kingwinner]

Homework Statement

"Let f(x)=x.
Define the change of variable y=5x.
Then this implies g(y)=y/5.
[we have g(y)=f(x(y))=f(y/5) and f(x)=g(y(x))=g(5x)] "

Homework Equations

N/A

The Attempt at a Solution

I don't understand the above statement.
If we define y=5x, then WHY does it imply g(y)=y/5? Shouldn't it be f(y)=y/5? WHY do we need to introduce a new function g? (here we are doing a change of variable on the independent variable x, how come the dependent variable also changes?)
Also, WHY do we have g(y)=f(x(y)) and f(x)=g(y(x))? I don't understand this.


I think my concepts in this topic of change of variables is screwed up. Can someone please explain?
Thank you!

 

[rock.freak667]

f(x)=x

if y=5x then x=y/5

so that f(y/5)=y/5 right?

since this is a function in y, we can call it g(y)

so g(y)=f(y/5)= y/5 ⇒ g(y)=y/5