(i) Each of the following apparently defines a function. However, each has one or more problems. Explain carefully what is wrong with each. (a) c : {cat, dog, rabbit, goat} → {black, brown, white, red} c(cat) = white, c(dog) = brown, c(rabbit) = brown, c(goat) = grey, c(cat) = black. (b) m : P({1,2, 3, ..., 100}) → {1,2, 3, . . , 100}, m(A) = the smallest element of A (ii) Let f and g be functions defined by f : R → R, g : N → N, g(x) = 5x – 4. f (x) = 5x – 4 (a) Prove carefully that f is bijective. (b) Prove carefully that a is not bijective.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1.
(i) Each of the following apparently defines a function. However, each has
one or more problems. Explain carefully what is wrong with each.
(a) c: {cat, dog, rabbit, goat} → {black, brown, white, red}
white, c(dog) = brown, c(rabbit) = brown,
c(goat) = grey, c(cat) = black.
(b) m : P({1, 2, 3, . , 100}) → {1, 2, 3, . . , 100}, m(A) = the smallest element of A
...
...
(ii) Let f and g be functions defined by
f : R → R, f(x) = 5x – 4
g : N → N, g(x) = 5x – 4.
(a) Prove carefully that f is bijective.
(b) Prove carefully that g is not bijective.
Transcribed Image Text:1. (i) Each of the following apparently defines a function. However, each has one or more problems. Explain carefully what is wrong with each. (a) c: {cat, dog, rabbit, goat} → {black, brown, white, red} white, c(dog) = brown, c(rabbit) = brown, c(goat) = grey, c(cat) = black. (b) m : P({1, 2, 3, . , 100}) → {1, 2, 3, . . , 100}, m(A) = the smallest element of A ... ... (ii) Let f and g be functions defined by f : R → R, f(x) = 5x – 4 g : N → N, g(x) = 5x – 4. (a) Prove carefully that f is bijective. (b) Prove carefully that g is not bijective.
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