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  3. 3 9 marks properties of functions let fr r be...

Question: 3 9 marks properties of functions let fr r be...

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3. [9 marks] Properties of functions. Let f:R -R be a function. Consider the following definitions. ·f is strictly increasing if and only if for every pair of real numbers z and y, if y then . f is strictly decreasing if and only if for every pair of real numbers r and y, if a < y then , f has a global maximum at z if and only if f(x) is always less than or equal to f(z), for every f(x) < f(v). f(x) >f(v). real number z. Translate each of the following statements into predicate logic. (a) The function fi is not strictly increasing. (You may use the variable fi in your translation.) (b) The function f2 is neither strictly increasing nor strictly decrcasing. (You may use the variable 2 in your translation.) your translation.) any real number. (c) The function fs has a global maximum at two different numbers. (You may use the variable fs in (d) For every function f : R → R, iff is strictly increasing then f does not have a global maximurn at
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