Affine transformation and coordinates of maps

[H Psi equal E Psi]

Hi everyone!

I'm having trouble with the following exercise:

Let $\mathrm {Aff}(ℝ)$ be the vector space of the affine maps from $ℝ$ to $ℝ$:
$$φ_{a,b}:ℝ→ℝ$$ $$x→a x + b$$

Find the contravariant and and covariant coordinate of the map:
$$φ_{1,1}:ℝ→ℝ$$ $$x→x + 1$$ with respect to the bases $\mathcal{B}:= \left\lbrace 2x,1 \right\rbrace$

Thank you for your help!

$\mathrm{H}Ψ=\mathrm{E}Ψ$

 

[WWGD]

Hi,
Maybe if you define for us the co- and contra- variant cordinates, we may be better able to help you; we may know (of) them by different names.