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Discrete Structures And Graph Theory

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2
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Show that function $f: \mathbf{R} \rightarrow\{x \in \mathbf{R}:-1<x<1\}$ defined by $f(x)=\frac{x}{1+|x|}, x \in \mathbf{R}$ is one-one and onto function.
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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Let $f: \mathrm{W} \rightarrow \mathrm{W}$ be defined as $f(n)=n-1$, if is odd and $f(n)=n+1$, if $n$ is even. Show that $f$ is invertible. Find the inverse of $f$. Here, $W$ is the set of all whole n
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $f(x)=10 x+7$. Find the function $g: \mathbf{R} \rightarrow \mathbf{R}$ such that $g$ o $f=f$ $\circ g=1_{\mathbf{R}}$.
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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Consider $f:\{1,2,3\} \rightarrow\{a, b, c\}$ given by $f(1)=a, f(2)=b$ and $f(3)=c$. Find $f^{-1}$ and show that $\left(f^{-1}\right)^{-1}=f$.
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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Consider $f: \mathbf{R}_{+} \rightarrow[-5, \infty)$ given by $f(x)=9 x^{2}+6 x-5 .$ Show that $f$ is invertible with $ f^{-1}(y)=\left(\frac{(\sqrt{y+6})-1}{3}\right) $
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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Show that $f$ is invertible with the inverse $f^{-1}$ of given $f$ by $f^{-1}(y)=\sqrt{y-4}$ where $\mathbf{R}_{+}$is the set of all non-negative real numbers.
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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Show that $f:[-1,1] \rightarrow \mathbf{R}$, given by $f(x)=\frac{x}{(x+2)}$ is one-one. Find the inverse of the function $f:[-1,1] \rightarrow$ Range $f$.
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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Let f, g and h be functions from R to R. Show that,
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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Find the area of the region lying inside, $ \begin{aligned} x^{2}+(y-1)^{2} &=1 \text { and outside,} \\\\ c^{2} x^{2}+y^{2} &=c^{2} \text { where } c=(\sqrt{2}-1) \end{aligned} $
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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Consider a set of integers from 1 to 250.
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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Relation and fuction
discrete structures and graph theory updated 2.6 years ago by prajapatijaimin • 3.2k
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