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

 Aug 15, 2021
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Suppose that f(x) and g(x) are functions on R such that the range of f is [-5,5], and the range of g is [-2,2]. The range of f(x) times g(x) is [a,b]. What is the largest possible value of b?

 

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\(-5\leq R_f\leq 5\\ -2\leq R_g\leq 2\\ \)

\(h(x)=f(x)\cdot g(x)\)

The smallest value that h (x) can, but does not have to have, is \(-2\cdot 5=\color{blue}-10.\)

The largest value that h (x) can, but does not have to have, is \(2\cdot 5=\color{blue}10.\)

You need the text of f(x) and g(x) because the maximum or minimum of the two functions can each be on a different x value.

laugh  !

 Aug 16, 2021

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