- #1

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## Homework Statement

T:R

_{2}[x] --> R

_{4}[x]

T(f(x)) = (x^3-x)f(x^2)

## Homework Equations

## The Attempt at a Solution

Let f(x) and g(x) be two functions in R2[x].

T(f(x) + g(x)) = T(f+g(x)) = (x^3-x)(f+g)(x^2) = (x^3-x)f(x^2) + (x^3-x)g(x^2) = T(f(x)) + T(g(x)).

let a be scalar in R:

aT(f(x)) = a(x^3-x)f(x^2) = (x^3-x)af(x^2) = T(af(x)).