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

 Aug 18, 2020
 #1
avatar+28021 
+2

I think this has been answered before...though I do not kow if I was correct.....this one is hard to read....

 

I believe the range could go as positive as   -5 x -2 = 10

   and as negative as -2 x 3 = -6

 

so  [-6,10]      Let me know if this is correct...or incorrect       (b would be '10' )

 Aug 18, 2020
 #2
avatar+58 
0

Thank you a lot! I solved it actually a little while ago, and that answer is right!

Williamjwu8  Aug 19, 2020
 #3
avatar+111626 
0

You sound surprised.

Melody  Aug 19, 2020

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