Question

Дана функция y=f(x), где f(x)=x² . При каких значениях x выполняеться равенство: f(x-1)=f(x-7)

Answer 1

Решение смотрите на фотографии

Answer 2

To find the values of x for which the equation f(x-1) = f(x-7) holds true, we need to set up and solve the equation.

Given that f(x) = x², let's substitute these expressions into the equation:

f(x-1) = f(x-7) (x-1)² = (x-7)²

Now, let's expand the expressions:

(x-1)² = x² - 2x + 1 (x-7)² = x² - 14x + 49

Now, set the two expanded expressions equal to each other:

x² - 2x + 1 = x² - 14x + 49

Next, move all terms to one side of the equation:

x² - x² - 2x + 14x = 49 - 1

Simplify:

12x = 48

Now, divide both sides by 12 to solve for x:

x = 48 / 12

x = 4

So, the value of x for which the equation f(x-1) = f(x-7) holds true is x = 4.