Yechish. va funksiyalarning qiymatlari sohasini qaraymiz.
Dastlab, ning qiymatlari sohasini aniqlaymiz:
Demak, funksiyaning qiymatlari sohasi bo’lar ekan. Bundan kelib chiqadiki, funksiya -2, -1, 0 va 1 sonlariga teng bo’la oladi, ya’ni
Endi funksiyaning qiymatlari sohasini qaraymiz.
Bizga ma’lumki, . Demak, , ya’ni . Demak, berilgan tengsizlik x ning haqiqiy sonlar to’plamidagi ixtiyoriy qiymatida o’rinli bo’ladi.
Javob: xϵR
1.3.20-misol. tengsizlikni yeching.
Yechish. Berilgan va funksiyalarning aniqlanish sohasini aniqlaymiz:
Demak, aniqlanish sohasida funksiyaning qiymatlari sohasi , hamda funksiyaning ham qiymatlari sohasi . Bundan kelib chiqadiki, aniqlanish sohasida, ya’ni oraliqda
tengsizlik doim o’rinli bo’ladi.
Javob:
1.3.21-misol. tengsizlikni yeching.
Yechish. va funksuyalarning aniqlanish sohasiga tegishli bo’lgan umumiy sonlarni topamiz:
Ularning aniqlanish sohasiga tegishli bo’lgan umumiy sonlar ![](data:image/png;base64,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)
Shu oraliqda funksiyaning qiymatlari sohasi , ya’ni .
funksiyaning qiymatlari sohasi esa , ya’ni .
Demak, berilgan tengsizlikning yechimi shu tengsizlikning aniqlanish sohasi bo’lar ekan.
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