Let f : A → B is one-one and its inverse f – 1 : B → A exists. If point ( α, β ) lies on y = f(x) then the point ( β, α ) lies on y = f –1 (x). Let 'm' be the minimum number of point of intersection of y = f(x) & y = f – 1 (x).
(i) If (1, 2) and (2, 1) lies on y = f –1 (x) and f(x) is continuous, then –
Text Solution
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Ans.
(i)
Sol. Since (1, 2) (2, 1) lie on y = f – 1 (x)
(2, 1), (1, 2) lie on y = f(x)
f(x) is continuous and (2, 1) and (1, 2) lie on opposite sides of y = x
∴ y = f(x) and y = f – 1 (x) must intersect at least one point on y = x ⇒ m = 3
(ii)
Sol.
From figure (1)
From figure (1) and (2)
From figure (2)
From figure (1)
(iii)
Sol.
f(x) = – x + sin x
From figure (3)
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