A simple application of a liner transformation

[trap101]

Let T: P₂(ℝ) --> P₂(ℝ) be defined by T(p(x)) = p( x-1)

a) Find the matrix of T with respect to the standard basis of P₂(ℝ)


Question: So I know how to do this for the most part, I'm just having a problem in terms of the constant 1 from the standard basis of {1, x , x² from P₂(ℝ). Applying the transformation to the constant 1; should i get a 0, or do I get the constant 1 back again?

Cheers

 

[micromass]

The constant 1 is actually the function

$$p:\mathbb{R}\rightarrow \mathbb{R}:x\rightarrow 1$$

From this, it is clear that indeed p(x-1)=1.

 

[trap101]

all I needed to know. Thanks a lot.