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यदि f: A → B तथा g: B → C एकैकी आच्छादक हैं तो gof: A → C है

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यदि f: A → B तथा g: B → C एकैकी आच्छादक हैं तो gof: A → C है

(A) एकैकी आच्छादक

(B) बहुएक आच्छादक

(C) एकैकी लेकिन आच्छादक नहीं

(D) बहुएक लेकिन आच्छादक नहीं

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सही विकल्प है (A) एकैकी आच्छादक

∵ f एकैकी है।

∴ यदि f(x1) = f(x2),तो

x1 = x2

∵ g भी एकैकी है।

तो, g(x1) = g(x2)

∴ x1 = x2

अब, gof(x1) = gof(x2)

g(f(x1)) = g(f(x2))

∵ g एकैकी है.

∴ f(x1) = f(x2)

जैसे कि f एकैकी है।

x1 = x2

अतः gof भी एकैकी है।

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