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Provide step-by-step explanations. Can I have some thoughts on how to explain the word "defined" used in the sentence? High accurate tutors, shorter answering time. 1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc. If it's an analysis course, I would interpret the word defined in this sentence as saying, "there's some function $f$, taking values in $\mathbb{R}$, whose domain is a subset of $\mathbb{R}$, and whatever the domain is, definitely it includes the closed interval $[a, b]$. Doubtnut helps with homework, doubts and solutions to all the questions. We write $f: A \to B$. Doubtnut is the perfect NEET and IIT JEE preparation App. The way I was taught, functions are things that have domains. 12 Free tickets every month. Unlimited access to all gallery answers. Always best price for tickets purchase. Therefore, The values for x at which f has a relative maximum are -3 and 4. Get solutions for NEET and IIT JEE previous years papers, along with chapter wise NEET MCQ solutions.
5, 2] or $1/x$ on [-1, 1]. It is a local maximum, meaning that it is the highest value within a certain interval, but it may not be the highest value overall. Anyhow, if we are to be proper and mathematical about this, it seems to me that the issue with understanding what it means for a function to be defined on a certain set is with whatever definition of `function' you are using. If it's just a precalculus or calculus course, I would just give examples of a nice looking formula that "isn't defined" on all of an interval, e. g. $\log(x)$ on [-. Grade 9 · 2021-05-18. For example, a function may have multiple relative maxima but only one global maximum. I support the point made by countinghaus that confusing a function with a formula representing a function is a really common error. Often "domain" means something like "I wrote down a formula, but my formula doesn't make sense everywhere. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year papers, NEET previous year papers, NCERT books for classes 6 to 12, CBSE, Pathfinder Publications, RD Sharma, RS Aggarwal, Manohar Ray, Cengage books for boards and competitive exams. Unlimited answer cards. However, I also guess from other comments made that there is a bit of a fuzzy notion present in precalculus or basic calculus courses along the lines of 'the set of real numbers at which this expression can be evaluated to give another real number'....?
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We may say, for any set $S \subset A$ that $f$ is defined on $S$. Check the full answer on App Gauthmath. For example, a measure space is actually three things all interacting in a certain way: a set, a sigma algebra on that set and a measure on that sigma algebra. We solved the question! I am having difficulty in explaining the terminology "defined" to the students I am assisting.
Tell me where it does make sense, " which I hate, especially because students are so apt to confuse functions with formulas representing functions. 31A, Udyog Vihar, Sector 18, Gurugram, Haryana, 122015. Gauthmath helper for Chrome. It's important to note that a relative maximum is not always an actual maximum, it's only a maximum in a specific interval or region of the function. Enjoy live Q&A or pic answer. Later on when things are complicated, you need to be able to think very clearly about these things. On plotting the zeroes of the f(x) on the number line we observe the value of the derivative of f(x) changes from positive to negative indicating points of relative maximum. To know more about relative maximum refer to: #SPJ4. Crop a question and search for answer.