Let L: C[0, 1] → C[0, 1] be a linear map. If L(1) =x, L(x) =x^2, then what is L(3x + 2)?

(2) Conjugate the map f(x) = 3x(1 – x) to a map of the form Q(x) = x² + c. Find the conjugacy map h and the value of c.

Suppose T : C^2 → C^3 is a linear map so that T(1, 1) = (1, 0, 2) and T(2, 3) = (1,−1, 4). What is T(8, 11)?

Letf : R² → R be defined by f((x, y)) = −7x − 9y. Is ƒ a linear transformation? a. f((x₁, y₁) + (x2, Y₂)) = as x1, etc.) f((x₁, y₁)) + f((x2, 3/2)) = Does f((x₁, y₁) + (x2, Y2 )) = f((x₁, y₁ )) + ƒ((x2, y2)) for all (x₁, y₁), (x2, y₂) € R²? choose + b. f(c(x, y)) = c(f((x, y))) = = Does f(c(x, y)) = c(f((x, y))) for all c E R and all (x, y) = R²? choose c. Isf a linear transformation? choose . (Enter X₁

Let L be a linear transformation from P₂ → R2x2 such that L(f) — ƒ(1) 0 Find dim[Range(L)] ƒ(2) [ƒ(2) ƒ(0)