Question

Решить фукцию f(x)=4x-20/x^2-5x

Answer 1

f(x) = (4x-20)/(x^2-5x)

Область определения данной функции совпадает с множеством решений неравенства x²-5x ≠ 0; x(x - 5) ≠ 0; x≠ 0; х ≠ 5.

Ответ: D(f) = (-∞; 0)U(0; 5)U(5; ∞)

Answer 2

To find the solution of the function $f(x) = \frac{4x-20}{x^2-5x}$, we need to determine the values of $x$ for which the function is defined and where it has a specific value.

To find the domain of the function (where it is defined), we need to identify the values of $x$ that would make the denominator $x^2-5x$ equal to zero. Since division by zero is undefined, we must exclude these values from the domain.

Step 1: Find the values that make the denominator zero. $x^2 - 5x = 0$

Step 2: Factor the equation, if possible. $x(x - 5) = 0$

Step 3: Find the solutions for $x$. Setting each factor to zero and solving for $x$: $x = 0$ or $x - 5 = 0$

So, $x = 0$ or $x = 5$ are the values that make the denominator zero.

Now, we need to consider the domain of the function, which is all real numbers except the values we found above. So, the domain of the function is $\mathbb{R} \setminus \{0, 5\}$.

Next, let's determine the value of the function at specific points. To do this, we can plug in different values of $x$ (within the domain) into the function.

For example:

1. $f(1) = \frac{4 \cdot 1 - 20}{1^2 - 5 \cdot 1} = \frac{-16}{-4} = 4$
2. $f(2) = \frac{4 \cdot 2 - 20}{2^2 - 5 \cdot 2} = \frac{-12}{-6} = 2$
3. $f(6) = \frac{4 \cdot 6 - 20}{6^2 - 5 \cdot 6} = \frac{4}{6} = \frac{2}{3}$

Remember, the value of the function is not defined at $x = 0$ and $x = 5$ due to the division by zero issue. For all other values of $x$ within the domain, you can plug them into the function to get the corresponding $f(x)$ values.