Merging man & maths https://www.mathcity.org/ Thu, 04 Jun 2026 17:20:52 +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/2 What is the value of pi? What is the value of $\pi$? * (A) 3.1415 * (B) $\frac{22}{7}$ * (C) $\frac{333}{160}$ * (D) None of these ✔ Answer The number π is a mathematical constant, the ratio of a circle's circumference to its diameter. It is an irrational number, meaning that it cannot be written as the ratio of two integers or in terminating or repeated decimals.$\pi=3.14159...$$\sqrt{2}=1.4142...$$e=2.718...$$\pi$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:25 +0000 https://www.mathcity.org/dyk/3 Its about square root [DYK] The reason is not difficult if one knows about the definition of square root of real numbers. Definition: Let $x$ be a non-negative number. Then a non-negative number $r$ is called square root of $x$ iff $r^2=x$. Square root of $x$ is denoted by $\sqrt{x}$$2^2=4$$3^2=9$$x$$r$$x$$r^2=x$$2^2=4$$(-2)^2=4$$\sqrt{4}=\sqrt{2^2}=\sqrt{(-2)^2}=2$$\sqrt{4}=\sqrt{2^2}=\sqrt{(-2)^2}=\pm 2$$\sqrt{4}$$\sqrt{x}$$x\geq0$$\sqrt{x}=x^{\frac{1}{2}}$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:27 +0000