3.6-bo'lim : Funktsiyalarni birlashtirish
1. Berilgan \(f\left( x \right) = 6x + 2\) va \(g\left( x \right) = 10 - 7x\) quyidagilardan har birini hisoblang.
- \(\left( {f - g} \right)\left( 2 \right)\)
- \(\left( {g - f} \right)\left( 2 \right)\)
- \(f\,g\)
- \(\displaystyle \left( {\frac{f}{g}} \right)\left( x \right)\)
a \(\left( {f - g} \right)\left( 2 \right)\) Yechim
Bu erda baholashdan tashqari ko'p narsa qilish kerak emas. Muayyan funktsiyani baholashni tekshirishni sizga qoldiramiz.
\[\left( {f - g} \right)\left( 2 \right) = f\left( 2 \right) - g\left( 2 \right) = 14 - \left( { - 4} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{18}}\]b \(\left( {g - f} \right)\left( 2 \right)\) Yechim
Bu erda baholashdan tashqari ko'p narsa qilish kerak emas. Muayyan funktsiyani baholashni tekshirishni sizga qoldiramiz.
\[\left( {g - f} \right)\left( 2 \right) = g\left( 2 \right) - f\left( 2 \right) = - 4 - 14 = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 18}}\]c \(f\,g\) Yechim
Bu erda baholashdan tashqari ko'p narsa qilish kerak emas. Shuni ham yodda tutingki, bu holda "baholash" haqiqatan ham har bir funktsiya uchun ikkita tenglamani kiritish va iloji bo'lsa javobni soddalashtirish uchun ba'zi asosiy algebraik manipulyatsiyalarni bajarishdan iborat.
\[f\,g = f\left( x \right)g\left( x \right) = \left( {6x + 2} \right)\left( {10 - 7x} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 42{x^2} + 46x + 20}}\]d \(\displaystyle \left( {\frac{f}{g}} \right)\left( x \right)\) Yechim
Bu erda baholashdan tashqari ko'p narsa qilish kerak emas. Shuni ham yodda tutingki, bu holda "baholash" haqiqatan ham har bir funktsiya uchun ikkita tenglamani kiritish va iloji bo'lsa, javobni soddalashtirish uchun ba'zi bir asosiy algebraik manipulyatsiyalarni bajarishdan iborat, garchi bu holda haqiqatan ham hech qanday soddalashtirish yo'q.
\[\left( {\frac{f}{g}} \right)\left( x \right) = \frac{{f\left( x \right)}}{{g\left( x \right)}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{6x + 2}}{{10 - 7x}}}}\]