(A) Function f:[0,π/3] → [0,1] defined by f(x) = √sin x is (p) one to one function

Question

Match the following:

(A) Function f:[0,π/3] → [0,1]  defined by f(x) = √sin x  is	(p) one to one function
(B) Function f:(1, ∞) → (1, ∞) defined by (x) = x + 3/x - 1  is	(q) many-one function
(C) Function f :[π/2, 4π/3] → [–1, 1] defined by f(x) = sinx is	(r) into function
(D) Function f:(2, ∞) → [8, ∞) defined by f(x) = x2 = x2/x - 2 is	(s) onto function

Answer 1

Correct option (A) → (p, r)(B) → (p, s), (C) → (q, s), (D) → (q, s)

f is one-to-one function.

Since

Hence, f is into function

Hence, f(x) is one to one. Since, x > 1.

Therefore, range of y = x + 3/x - 1 is (1,∞)

Hence, f is onto function.

(C) See Fig

From graph, f(x) is many-one and onto.

Therefore, f ′(x) < 0 if 2 < x < 4 and f ′(x) > 0 if x > 4.

f(x) is many-one.

f(4) = 8 (is the least value of f(x))

Therefore, range = [8, ∞) Therefore, f(x) is onto.