How to shift the function xe^x mathematically by one unit on the x axis?

[bugatti79]

Hi Folks,

I have a function $$x {e^{-x}}$$ and if i shift it one unit to the right on the x-axis we have $$(x-1) {e^{-(x-1)}}$$

How do I show this mathematically?

Even consider the simple case of x^2, if we shift by 1 unit to the right it becomes (x-1)^2

What is the method mathematically?

Regards

 

[MarkFL]

Suppose $f(x)$ has a root at $x=a$, i.e., $f(a)=0$. Then $f(x-h)$ will have a root at $x-h=a$, or $x=a+h$. Thus, the function $f$ has been shifted $h$ units to the right.