Constrained function?

Calculus Level 5

Consider the function f ( x ) f(x) which has no real roots. If f ( e ) = π f(e) = \pi , then in what quadrants can f ( x ) f(x) be in?

Note that f ( x ) f(x) is said to be in a quadrant if there is a point ( x , f ( x ) ) (x,f(x)) in that quadrant.

I & II only I & IV only I only I, II, III, & IV

Francisco Rivera by Francisco Rivera , 24, USA

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1 solution

Francisco Rivera
Mar 4, 2016

The crux of the problem lies in realizing that there is no specification that the function is continuous. Thus, we can construct a piece-wise function that never has a zero, yet is in all quadrants.

12 Helpful 0 Interesting 0 Brilliant 0 Confused

Hey!! I assumed it to be continous

Aakash Khandelwal - 5 years, 3 months ago

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