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Найдите значение выражения \( 5(p(2 x)-2 p(x+5)) \), если \( p(x)=x-10 \). Спрятать решение

Ask by Guerrero Sullivan. in Russia
Mar 15,2025

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Чтобы найти значение выражения \( 5(p(2 x)-2 p(x+5)) \) при \( p(x) = x - 10 \), сначала подставим \( x \) в функцию \( p \): 1. Найдём \( p(2x) \): \[ p(2x) = 2x - 10 \] 2. Найдём \( p(x+5) \): \[ p(x+5) = (x+5) - 10 = x - 5 \] Теперь, подставим найденные значения в выражение: \[ 5(p(2x) - 2p(x+5)) = 5((2x - 10) - 2(x - 5)) \] Упростим выражение: \[ = 5(2x - 10 - 2x + 10) = 5(0) = 0 \] Таким образом, значение выражения равно \( 0 \).

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