Merging man & maths https://www.mathcity.org/ Fri, 05 Jun 2026 04:41:48 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/dyk/1 Are the functions are same? [Are the functions are same?] Consider two functions $f(x)=x+3$ and $\displaystyle g(x)=\frac{x^2-9}{x-3}$. Is $f=g$? Answer A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Set of inputs is usually know as $f:A \to B$$f = A$$B$$A$$A$$B$$A=\mathbb{N}$$B=\mathbb{R}$$f(x)=x+1$$1 \mapsto 2$$\quad 2 \mapsto 3$$\quad 3 \mapsto 4$$f = \mathbb{N}$$A=\mathbb{R}$$B=\mathbb… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:25 +0000 https://www.mathcity.org/dyk/4 Is it difficult to answer? 1−−−0.999… [Is 1=0.999...?] This is a simple and common question asked to students, who have passed higher secondary school certificate. Most of the student unable to give the correct answer. Well, we cannot predict the exact reason but one simple reason seems to be a lack of logical reasoning. For example, if we wish to round off $0.999...$$x=0.999...$$10x=9.99...$$10x=9+0.999...$$10x=9+x$$9x=9$$x=1$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:28 +0000