Question

Дана функция y = f(x), где f(x) = 2x² + x – 1. При каком значении аргумента выполняется равенство f(x - 3) = f(x + 3)?

Answer 1

Ответ:

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Объяснение:

Answer 2

Problem Analysis

We are given a function f(x) = 2x² + x - 1 and we need to find the value of x for which f(x - 3) = f(x + 3).

Solution

To find the value of x that satisfies the equation f(x - 3) = f(x + 3), we need to substitute the expressions for f(x - 3) and f(x + 3) into the equation and solve for x.

Let's start by substituting x - 3 into the function f(x): f(x - 3) = 2(x - 3)² + (x - 3) - 1

Next, let's substitute x + 3 into the function f(x): f(x + 3) = 2(x + 3)² + (x + 3) - 1

Now, we can set these two expressions equal to each other and solve for x: 2(x - 3)² + (x - 3) - 1 = 2(x + 3)² + (x + 3) - 1

Simplifying the equation: 2(x² - 6x + 9) + (x - 3) - 1 = 2(x² + 6x + 9) + (x + 3) - 1

Expanding and combining like terms: 2x² - 12x + 18 + x - 3 - 1 = 2x² + 12x + 18 + x + 3 - 1

Simplifying further: 2x² - 11x + 14 = 2x² + 13x + 20

Subtracting 2x² from both sides: -11x + 14 = 13x + 20

Subtracting 13x from both sides: -24x + 14 = 20

Subtracting 14 from both sides: -24x = 6

Dividing both sides by -24: x = -6/24

Simplifying the fraction: x = -1/4

Therefore, the value of x that satisfies the equation f(x - 3) = f(x + 3) is x = -1/4.

Answer

The value of the argument x for which the equation f(x - 3) = f(x + 3) is satisfied is x = -1/4.