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847
Kenneth Rosen Edition 7 Exercise 2.3 Question 57 (Page No. 154)
Let $a$ and $b$ be real numbers with $a<b$. Use the floor and / or ceiling functions to express the number of integers $n$ that satisfy the inequality $a<n<b.$
Let $a$ and $b$ be real numbers with $a<b$. Use the floor and / or ceiling functions to express the number of integers $n$ that satisfy the inequality $a<n<b.$
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848
Kenneth Rosen Edition 7 Exercise 2.3 Question 56 (Page No. 154)
Let $a$ and $b$ be real numbers with $a<b$. Use the floor and / or ceiling functions to express the number of integers $n$ that satisfy the inequality $a≤n≤b$.
Let $a$ and $b$ be real numbers with $a<b$. Use the floor and / or ceiling functions to express the number of integers $n$ that satisfy the inequality $a≤n≤b$.
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850
Kenneth Rosen Edition 7 Exercise 2.3 Question 54 (Page No. 154)
Prove that if $x$ is a reall number , then $\left \lfloor -x \right \rfloor = - \left \lceil x \right \rceil$ and$\left \lceil -x \right \rceil = -\left \lfloor x \right \rfloor$
Prove that if $x$ is a reall number , then $\left \lfloor -x \right \rfloor = - \left \lceil x \right \rceil$ and$\left \lceil -x \right \rceil = -\left \lfloor x \right ...
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852
Kenneth Rosen Edition 7 Exercise 2.3 Question 52 (Page No. 154)
Show that if $x$ is a real number and $n$ is an integer, then $x\leq n$ if and only if $\left \lceil x \right \rceil \leq n$ $n\leq x$ if and only if $ n\leq \left \lfloor x \right \rfloor $
Show that if $x$ is a real number and $n$ is an integer, then$x\leq n$ if and only if $\left \lceil x \right \rceil \leq n$$n\leq x$ if and only if $ n\leq \left \lfloor ...
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853
Kenneth Rosen Edition 7 Exercise 2.3 Question 51 (Page No. 154)
Show that if $x$ is a real number and $n$ is an integer, then $x<n$ if and only if $\left \lfloor x \right \rfloor < n$ $n<x$ if and only if $ n<=\left \lfloor x \right \rfloor $
Show that if $x$ is a real number and $n$ is an integer, then$x<n$ if and only if $\left \lfloor x \right \rfloor < n$$n<x$ if and only if $ n<=\left \lfloor x \right \rf...
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854
Kenneth Rosen Edition 7 Exercise 2.3 Question 50 (Page No. 154)
Show that if $x$ is a real number, and $m$ is an integer, then $\left \lceil x+m \right \rceil = \left \lceil x \right \rceil +m.$
Show that if $x$ is a real number, and $m$ is an integer, then $\left \lceil x+m \right \rceil = \left \lceil x \right \rceil +m.$
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857
Kenneth Rosen Edition 7 Exercise 2.3 Question 47 Page No. 154)
Show that $\left \lceil x-1/2 \right \rceil$ is the closest integer to the number $x$,except when $x$ is midway between two integers, when it is the smaller of these two integers
Show that $\left \lceil x-1/2 \right \rceil$ is the closest integer to the number $x$,except when $x$ is midway between two integers, when it is the smaller of these two ...
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858
Kenneth Rosen Edition 7 Exercise 2.3 Question 46 (Page No. 154)
Show that $\left \lfloor x+1/2 \right \rfloor$ is the closest integer to the number $x$,except when $x$ is midway between two integers, when it is the larger of these two integers
Show that $\left \lfloor x+1/2 \right \rfloor$ is the closest integer to the number $x$,except when $x$ is midway between two integers, when it is the larger of these two...
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860
Kenneth Rosen Edition 7 Exercise 2.3 Question 44 (Page No. 154)
Let $f$ be a function from $A$ to $B$. Let $S$ and $T$ be subsets of $B$. Show that $f^{-1}(S \cup T) = f^{-1}(S) \cup f^{-1}(T)$ $f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$
Let $f$ be a function from $A$ to $B$. Let $S$ and $T$ be subsets of $B$. Show that$f^{-1}(S \cup T) = f^{-1}(S) \cup f^{-1}(T)$$f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(...
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861
Kenneth Rosen Edition 7 Exercise 2.3 Question 43 (Page No. 154)
Let $g(x) = \left \lfloor x \right \rfloor$. Find $g^{-1}(\left \{ 0 \right \})$ $g^{-1}(\left \{ -1,0,1 \right \})$ $g^{-1}(\left \{ x|0<x<1 \right \})$
Let $g(x) = \left \lfloor x \right \rfloor$. Find$g^{-1}(\left \{ 0 \right \})$$g^{-1}(\left \{ -1,0,1 \right \})$$g^{-1}(\left \{ x|0<x<1 \right \})$
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862
Kenneth Rosen Edition 7 Exercise 2.3 Question 42 (Page No. 154)
Let $f$ be the function from $R$ to $R$ defined by $f(x) = x^2$. Find $f^{-1}(\left \{ 1 \right \})$ $f^{-1}(\left \{ x|0<x<1 \right \})$ $f^{-1}(\left \{ x|x>4 \right \})$
Let $f$ be the function from $R$ to $R$ defined by $f(x) = x^2$. Find$f^{-1}(\left \{ 1 \right \})$$f^{-1}(\left \{ x|0<x<1 \right \})$$f^{-1}(\left \{ x|x>4 \right \})$
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863
Kenneth Rosen Edition 7 Exercise 2.3 Question 40 (Page No. 154)
Let $f$ be a function from the set $A$ to the set $B$. Let $S$ adn$T$ be subsets of $A$ .Show that $f(S \cup T) = f(S) \cup f(T)$ $f(S \cap T) = f(S) \cap f(T)$
Let $f$ be a function from the set $A$ to the set $B$. Let $S$ adn$T$ be subsets of $A$ .Show that$f(S \cup T) = f(S) \cup f(T)$$f(S \cap T) = f(S) \cap f(T)$
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864
Kenneth Rosen Edition 7 Exercise 2.3 Question 39 (Page No. 154)
Show that the function $f(x)=ax+b$ from $R$ to $R$ is invertible, where $a$ and $b$are constants, with $a=0$, and find the inverse of $f$.
Show that the function $f(x)=ax+b$ from $R$ to $R$ is invertible, where $a$ and $b$are constants, with $a=0$, and find the inverse of $f$.
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865
Kenneth Rosen Edition 7 Exercise 2.3 Question 38 (Page No. 154)
Let $f(x) = ax+b$ and $g(x) =cx+d$, where a,b,c, and d ar constants. Determine neccessary and sufficient conditions on the constants a,b,c, and d so that $fog =gof$
Let $f(x) = ax+b$ and $g(x) =cx+d$, where a,b,c, and d ar constants. Determine neccessary and sufficient conditions on the constants a,b,c, and d so that $fog =gof$
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