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Q.

Statement-1: f : R → R is a function defined by f(x) = 5x + 3. If g = f-1, then g(x) = x - 3 5. Statement-2: If f : A→ B is a bijection and g : B → A is the inverse of f, then fog is the identity function on A.

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a

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

b

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

c

STATEMENT-1 is True, STATEMENT-2 is False

d

STATEMENT-1 is False, STATEMENT-2 is True

answer is C.

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Detailed Solution

Let y=5x+3⇒x=y−35→ g(x) = x - 35 is the inverse of f, so statement-1 is TrueStatement-2 is false because g : B → A and f : A → B ⇒ fog : B→ B and g = f-1 ⇒fog is an identity function on B.
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