Let and be two functions

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let f:A→Bf:A\to B and g:B→Cg:B\to C be two functions. Which one of the following conditions is necessary and sufficient for the composition g∘fg\circ f to be well-defined? (a) Dom⁡(f)⊆Dom⁡(g)\operatorname{Dom}(f)\subseteq\operatorname{Dom}(g) (b) Dom⁡(f)⊆Ran⁡(g)\operatorname{Dom}(f)\subseteq\operatorname{Ran}(g) (c) Ran⁡(f)⊆Dom⁡(g)\operatorname{Ran}(f)\subseteq\operatorname{Dom}(g) (d) Dom⁡(g)⊆Ran⁡(f)\operatorname{Dom}(g)\subseteq\operatorname{Ran}(f)

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