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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. 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 [-. Often "domain" means something like "I wrote down a formula, but my formula doesn't make sense everywhere. 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.

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Get all the study material in Hindi medium and English medium for IIT JEE and NEET preparation. Crop a question and search for answer. The way I was taught, functions are things that have domains. If $(x, y) \in f$, we write $f(x) = y$.

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To unlock all benefits! Therefore, The values for x at which f has a relative maximum are -3 and 4. 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'....? 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. 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. 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. We may say, for any set $S \subset A$ that $f$ is defined on $S$. I am having difficulty in explaining the terminology "defined" to the students I am assisting. Check the full answer on App Gauthmath. Can I have some thoughts on how to explain the word "defined" used in the sentence? 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. 12 Free tickets every month. We write $f: A \to B$. I agree with pritam; It's just something that's included.

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Unlimited answer cards. Gauthmath helper for Chrome. 5, 2] or $1/x$ on [-1, 1]. High accurate tutors, shorter answering time. Here is the sentence: If a real-valued function $f$ is defined and continuous on the closed interval $[a, b]$ in the real line, then $f$ is bounded on $[a, b]$. It has helped students get under AIR 100 in NEET & IIT JEE. 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. Unlimited access to all gallery answers. To know more about relative maximum refer to: #SPJ4. NCERT solutions for CBSE and other state boards is a key requirement for students. A function is a domain $A$ and a codomain $B$ and a subset $f \subset A\times B$ with the property that if $(x, y)$ and $(x, y')$ are both in $f$, then $y=y'$ and that for every $x \in A$ there is some $y \in B$ such that $(x, y) \in f$. Gauth Tutor Solution.

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Enjoy live Q&A or pic answer. A relative maximum is a point on a function where the function has the highest value within a certain interval or region. In general the mathematician's notion of "domain" is not the same as the nebulous notion that's taught in the precalculus/calculus sequence, and this is one of the few cases where I agree with those who wish we had more mathematical precision in those course. Tell me where it does make sense, " which I hate, especially because students are so apt to confuse functions with formulas representing functions. Ask a live tutor for help now. Doubtnut is the perfect NEET and IIT JEE preparation App.

Always best price for tickets purchase. We solved the question! 31A, Udyog Vihar, Sector 18, Gurugram, Haryana, 122015. For example, a function may have multiple relative maxima but only one global maximum.