And the relation $g$ is defined by \[g(x)=\left\{ \begin{matrix} {{x}^{2}},0\le x\le 2 \\ 3x,2\le x\le 10 \\ \end{matrix} \right.\] Show that $f$ is a function and $g$ is not a function. Ans:According to the problem, we have the function $f$ as, $f(x)...
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Function as special case of relation Function as mapping, codomain, domain Different range of functions Even/odd functions Into/onto/one-to-one functions All special functions Difference, product, sum, & composition of functions Invertible functions Chapter 2: Algebra Complex number algebra ...
The difference between relation and function is the same if it is a continuous domain or whether it is discrete domain. To be a function each x value gives one y value you. Just because the x value is isolated it doesn't change the requirement to be a function. If you were ...
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Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the set of reals with itself (upto R x R x R).Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a specia...
Redox Reaction Notes Function Notes Nomenclature of Organic Compounds Notes Quadratic Equations Notes Mathematical Tools Notes Determinants Notes JEE Study Plan Don’t start planning your studies straight away. Establish manageable, early goals that you may gradually raise as time goes on. You can creat...
GP & English Tutor with First Class Honours, NUS [Writer’s note: While this article is addressed specifically to Singapore-based students, it may hold some truth for students in many other places as well.] Dear young friend, I’m writing this to share some thoughts that I used to convey...
Let , and partition the 8 elements of into equivalence classes as follows: The resulting equivalence relation clearly satisfies (PS1), since , , and are all in the same equivalence class. As for (PS2), you can scan the above equations and verify that for each , each of the three ...