A Line Missing a Composite Step Function
Difficulty: Hard · Topics: Algebra, Functions, Piecewise Functions
Kompozit pog‘onali funksiyani kesmaydigan to‘g‘ri chiziq
The graph of y=f(x) is shown below, and g(x)=(f° f)(x).
graph "x":[-1.6,3.6],"y":[-2.8,2.8],"xTicks":[1,2],"yTicks":[-2,-1,1,2],"label":"Step graph of y = f(x): value 2 for x below 1, f(1) = -1, value -2 on 1 < x <= 2, value 1 for x above 2","items":["type":"ray","from":[1,2],"to":[-1.5,2],"start":"open","type":"point","at":[1,-1],"type":"line","from":[1,-2],"to":[2,-2],"start":"open","end":"closed","type":"ray","from":[2,1],"to":[3.5,1],"start":"open","type":"guide","at":[1,2],"to":"x","type":"guide","at":[2,1],"type":"label","at":[2.9,1.75],"text":"y = f(x)"]
Find the range of the real number a (a≠ 0) for which the line y=ax+1 does not meet the graph of y=g(x).
y=f(x) ning grafigi quyida ko‘rsatilgan va g(x)=(f° f)(x).
graph "x":[-1.6,3.6],"y":[-2.8,2.8],"xTicks":[1,2],"yTicks":[-2,-1,1,2],"label":"Step graph of y = f(x): value 2 for x below 1, f(1) = -1, value -2 on 1 < x <= 2, value 1 for x above 2","items":["type":"ray","from":[1,2],"to":[-1.5,2],"start":"open","type":"point","at":[1,-1],"type":"line","from":[1,-2],"to":[2,-2],"start":"open","end":"closed","type":"ray","from":[2,1],"to":[3.5,1],"start":"open","type":"guide","at":[1,2],"to":"x","type":"guide","at":[2,1],"type":"label","at":[2.9,1.75],"text":"y = f(x)"]
y=ax+1 to‘g‘ri chiziq y=g(x) grafigini kesmaydigan haqiqiy a (a≠ 0) sonning qiymatlar oralig‘ini toping.