Q2 of 215 Page 3

Which one of the following graphs represent a one-one function?


Formula:-


(i) A function is one-one function or an injection if


f(x)=f(y)


⇒ x=y for all x, y ∈ A


or f(x)f(y)


⇒ xy for all x, y ∈ A


(a) It is not one-one function as it has same image on x axis


(b) It is one-one function s it have unique image


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If f : A → A and g : A → A are two bijections, then prove that

(i) fog is an injection


(ii) fog is a surjection

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If A = {1, 2, 3} and B = {a, b}, write total number of functions from A to B.

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If A = {a, b, c} and B = {–2, –1, 0, 1, 2}, write total number of one-one functions from A to B.