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571
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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574
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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575
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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577
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)$$f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(...
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578
Kenneth Rosen Edition 7 Exercise 2.3 Question 43 (Page No. 154)
Let $g(x) = \left \lfloor x \right \rfloor$. Find $g^{-1}(\left \{ 0 \right \})$ $g^{-1}(\left \{ -1,0,1 \right \})$ $g^{-1}(\left \{ x|0<x<1 \right \})$
Let $g(x) = \left \lfloor x \right \rfloor$. Find$g^{-1}(\left \{ 0 \right \})$$g^{-1}(\left \{ -1,0,1 \right \})$$g^{-1}(\left \{ x|0<x<1 \right \})$
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579
Kenneth Rosen Edition 7 Exercise 2.3 Question 42 (Page No. 154)
Let $f$ be the function from $R$ to $R$ defined by $f(x) = x^2$. Find $f^{-1}(\left \{ 1 \right \})$ $f^{-1}(\left \{ x|0<x<1 \right \})$ $f^{-1}(\left \{ x|x>4 \right \})$
Let $f$ be the function from $R$ to $R$ defined by $f(x) = x^2$. Find$f^{-1}(\left \{ 1 \right \})$$f^{-1}(\left \{ x|0<x<1 \right \})$$f^{-1}(\left \{ x|x>4 \right \})$
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580
Kenneth Rosen Edition 7 Exercise 2.3 Question 40 (Page No. 154)
Let $f$ be a function from the set $A$ to the set $B$. Let $S$ adn$T$ be subsets of $A$ .Show that $f(S \cup T) = f(S) \cup f(T)$ $f(S \cap T) = f(S) \cap f(T)$
Let $f$ be a function from the set $A$ to the set $B$. Let $S$ adn$T$ be subsets of $A$ .Show that$f(S \cup T) = f(S) \cup f(T)$$f(S \cap T) = f(S) \cap f(T)$
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581
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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582
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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589
Kenneth Rosen Edition 7 Exercise 2.3 Question 30 (Page No. 154)
Let $S= \left \{ -1,0,2,4,7 \right \}$. Find $f(S)$ if $f(x) =1$ $f(x) = 2x+1$ $f(x) =\left \lceil x/5 \right \rceil$ $f(x) = \left \lfloor (x^2+1)/3 \right \rfloor$
Let $S= \left \{ -1,0,2,4,7 \right \}$. Find $f(S)$ if$f(x) =1$$f(x) = 2x+1$$f(x) =\left \lceil x/5 \right \rceil$$f(x) = \left \lfloor (x^2+1)/3 \right \rfloor$
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2 answers
592
Kenneth Rosen Edition 7 Exercise 2.3 Question 27 (Page No. 153)
Prove that a strictly decreasing function from $R$ to it-self is one-to-one. Give an example of an decreasing function from $R$ to itself that is not one-to-one
Prove that a strictly decreasing function from $R$ to it-self is one-to-one.Give an example of an decreasing function from $R$ to itself that is not one-to-one
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593
Kenneth Rosen Edition 7 Exercise 2.3 Question 26 (Page No. 153)
Prove that a strictly increasing function from $R$ to it-self is one-to-one. Give an example of an increasing function from $R$ to itself that is not one-to-one
Prove that a strictly increasing function from $R$ to it-self is one-to-one.Give an example of an increasing function from $R$ to itself that is not one-to-one
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594
Kenneth Rosen Edition 7 Exercise 2.3 Question 25 (Page No. 153)
Let $f: R \rightarrow R$ and let $f(x) >0$ for all $x \epsilon R.$ Show that $f(x) $ is strictly decreasing if and only if the function $g(x) = 1/f(x)$ is strictly increasing.
Let $f: R \rightarrow R$ and let $f(x) >0$ for all $x \epsilon R.$ Show that $f(x) $ is strictly decreasing if and only if the function $g(x) = 1/f(x)$ is strictly incre...
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595
Kenneth Rosen Edition 7 Exercise 2.3 Question 24 (Page No. 153)
Let $f: R \rightarrow R$ and let $f(x) >0$ for all $x \epsilon R.$ Show that $f(x) $ is strictly increasing if and only if the function $g(x) = 1/f(x)$ is strictly decreasing.
Let $f: R \rightarrow R$ and let $f(x) >0$ for all $x \epsilon R.$ Show that $f(x) $ is strictly increasing if and only if the function $g(x) = 1/f(x)$ is strictly decrea...
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