Question

G(x) = log0.12(7 + 6x-x²);​

Answer 1

Ответ:

(-7;-1)

Пошаговое объяснение:

g(x) = log0.12(7 + 6x-x²);​

Область определения функции:

7 + 6x-x²​больше0

-x²+6х+7=0

Д=в²-4*а*с=36-4*7*(-1)=36+28=64=8²

х1=(-6+8):(-2)=-1

х2=(-6-8):(-2)=-7

Это парабола ветви которой направлены вниз.   Отметим на числовом луче точки -7 и -1. Так как 7 + 6x-x²​больше 0, то решение лежит выше оси ОХ. Тогда получим ответ: х принадлежит  (-7;-1)

Answer 2

It seems like you have provided a function G(x) that involves logarithms with a base of 0.12 and some algebraic expressions. To work with this function, we can break it down step by step.

The given function is:

G(x) = log₀.₁₂(7 + 6x - x²)

First, let's simplify the expression inside the logarithm:

1. 7 + 6x - x²

Next, we can factor the quadratic expression:

2. -(x² - 6x - 7)

Now, let's factor the quadratic expression further:

3. -(x² - 6x - 7) = -(x² - 7x + x - 7) = -(x(x - 7) + 1(x - 7))

Now, we have factored the expression as a product of two binomials:

4. -(x - 7)(x + 1)

So, the expression inside the logarithm is -(x - 7)(x + 1). Now, we can rewrite the function G(x):

G(x) = log₀.₁₂(-(x - 7)(x + 1))

Now, you can evaluate this function for specific values of x. If you have any specific values of x for which you want to calculate G(x), please provide them, and I can help you find the corresponding values of G(x).