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Suppose that f(x) and g(x) are functions  on {R} such that the range of f is [-5,3], and the range of g is [-2,1]. The range of f(x).g(x) is [a,b]. What is the largest possible value of b?

 Mar 3, 2020
edited by Alan  Mar 3, 2020
 #1
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The largest possible value of b is 1*3 = 3.

 Mar 3, 2020
 #2
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The smallest value of f is -5, that of g is -2.  The product of these is +10, so 10 is the maximum value of b.  Here is one of an infinite number of possible examples:

 

 Mar 3, 2020

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