Which of the following define linear operators on the vector space C1(R) of continuously differentiable scalar functions What is the target space (a) L f f(0) f(1) (b) L f f(0) f(1) (c) L f1 f sup2 (1) (d) L f f sup2 (3) f(2) (e) L f x2 f(x) (f) L f f(x 2) (g) L f f(x) 2 (h) L f f sup2 (2x) (i) L f f sup2 (x2) (j) L f f(x) sinx f sup2 (x) cosx (k) L f 2 log f(0) (1) (m) (n) (o) (p) (q) (r) (s) LIflfy)dy Lifi) dy

Question: Which of the following define linear operators on the vector space C1(R) of continuously differentiable scalar functions? What is the target space? (a) L[f] =

Which of the following define linear operators on the vector space C1(R) of continuously differentiable scalar functions? What is the target space?
(a) L[f] = f(0) + f(1)
(b) L[f] = f(0) f(1)
(c) L[f1 = f€²(1)
(d) L[f] = f€²(3) - f(2)
(e) L[f] = x2 f(x)
(f) L[f] = f(x + 2)
(g) L[f] = f(x) + 2
(h) L[f] = f€²(2x)
(i) L[f] = f€²(x2)
(j) L[f] = f(x) sinx - f€²(x) cosx
(k) L[f] = 2 log f(0)
(1)

(m)

(n)

(o)

(p)

(q)

(r)

(s)

LIflfy)dy Lifi) dy

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