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Kenneth Rosen Edition 7 Exercise 2.3 Question 28 (Page No. 153)
Pooja Khatri
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Show that the function $f(x)=e^x $ from the set of real numbers to the set of real numbers is not invertible, but if the codomain is restricted to the set of positive real numbers, the resulting function is invertible
kenneth-rosen
discrete-mathematics
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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
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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
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265
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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.
Pooja Khatri
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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.
Pooja Khatri
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Apr 9, 2019
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Pooja Khatri
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kenneth-rosen
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