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

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SUMMARY

The mathematical method for shifting a function one unit to the right on the x-axis involves substituting the variable x with (x-1). For the function f(x) = x e^{-x}, the shifted function becomes f(x-1) = (x-1) e^{-(x-1)}. This principle applies universally, as demonstrated with the polynomial function f(x) = x^2, which transforms to f(x-1) = (x-1)^2 when shifted. The general rule states that if f(x) has a root at x=a, then f(x-h) has a root at x=a+h.

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bugatti79
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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
 
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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.
 

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