Which of the following functions from Z to Z are bijections-a fx-x3b fx-x-2c fx-2 x-1d fx-x2-1

Given: f : Z nbsp; rarr; Z (a) nbsp;f(x) = nbsp;x3 It is one one but not onto. Thus, it is not bijective. (b) nbsp;f(x) = nbsp;x nbsp;+ 2 It ...

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Bijective Fuction

Which of the ...

Question

Which of the following functions from Z to Z are bijections?
(a) f(x) = x³
(b) f(x) = x + 2
(c) f(x) = 2x + 1
(d) f(x) = x² + 1

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Z \to Z

f (x) = x^{3}

f (x) = 2 x + 1

How many of the following pairs of function are identcal

(a) f (x) = $\frac{x^{2}}{x}, g (x) = x$

(b) f(x) = $\frac{x^{2} - 1}{x - 1}$ g(x) = x + 1

(d) $f (x) = \frac{x}{x^{2}}, g (x) = \frac{1}{x}$

How many of the following pairs of function are identcal

(a) $f (x) = \frac{x^{2}}{x}, g (x) = x$

(b) $f (x) = \frac{x^{2} - 1}{x - 1}, g (x) = x + 1$

(d) $f (x) = \frac{x}{x^{2}}, g (x) = \frac{1}{x}$

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