Consider f : {4, 5, 6} → {p, q, r} given by f (4) = p, f (5) = q, f

1.	Consider f : {4, 5, 6} → {p, q, r} given by f (4) = p, f (5) = q, f (6) = r. Find the inverse of f i.e., f –1 and show that (f –1) –1 = f.
Answer» Given, f : {4, 5, 6} → {p, q, r} such that f(4) = p, f (5) = q, f (6) = r ⇒ f = {4, p), (5, q), (6, r)} (f defined by ordered pairs) ⇒ f is one-one and onto ⇒ f^–1 exists ⇒ f ^–1 = {(p, 4), (q, 5), (r, 6)} (∵ components of ordered pains are interchanged in case of inverse functions) ⇒ (f ^–1)^–1 = {(4, p), (5, q), (6, r)} = f

Consider f : {4, 5, 6} → {p, q, r} given by f (4) = p, f (5) = q, f (6) = r. Find the inverse of f i.e., f –1 and show that (f –1) –1 = f.

Answer»

Given,

f : {4, 5, 6} → {p, q, r} such that

f(4) = p, f (5) = q, f (6) = r

⇒ f = {4, p), (5, q), (6, r)} (f defined by ordered pairs)

⇒ f is one-one and onto

⇒ f^–1 exists

⇒ f ^–1 = {(p, 4), (q, 5), (r, 6)}

(∵ components of ordered pains are interchanged in case of inverse functions)

⇒ (f ^–1)^–1 = {(4, p), (5, q), (6, r)}

= f