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1. What is the Difference Between Range and Co domain of Function ?

2.If i say a function is one to one , onto , bijection what does it actually tell about the function is there any significance or they are just types of function ?

3. when i say $fog(x)$ then $fog(x) = f(g(x))$ we know that $g(x)$ need not be onto i understand why but why its must that f should be onto. One reason could be: if f is onto then the range of $fog(x) =$ $\text{function f}$ ,   but that doesn't make sense because say if in co domain of f there is an element which doesn't have any pre image in domain then what's the problem because we can never attain that image because there exist no pre image so how does it effect its range ?

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1. What is the Difference Between Range and Co domain of Function ?
 

Range is the actual values that are images of Domain. Whereas Co-Domain is  everything that you have on right side of any function.

For example, when we write $f : A \rightarrow B$ then A is Domain, B is Co-domain and the Set $R = \left \{ f(x) \,|\,x \in A \right \}$ is Range.

Say, $f : \mathbb{R} \rightarrow \mathbb{R}$ and $f(x) = e^x$ then here $\mathbb{R}$ is Co-domain and $(0, ∞ )$ is Range of $f$.


2.If i say a function is one to one , onto , bijection what does it actually tell about the function is there any significance or they are just types of function ?

Of course there is significance. In Mathematics, Functions are one the Most important concepts. To see just a glimpse of their (injection, bijection, surjection etc) significance.. refer here : https://gateoverflow.in/216802/set-theory


when i say fog(x) then fog(x) = f(g(x)) we know that g(x) need not be onto i understand why but why its must that f should be onto.

Who said that for $fog$ to be defined, $f$ must be Onto function?? It's not necessary. Neither $f$ nor $g$ have to be onto for $fog$ or $gof$ to be defined.

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imagine an circle,co domain is the complete circle and range is a part of it.

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