Question

Найти область значений функции

Answer 1

Функция у=1/x²  →0 при  х→∞   и  →∞ при х→0
поэтому 1/х²→1 при х→∞

область значений у∈(1;∞)

Answer 2

Finding the Range of a Function

To find the range of a function, we need to determine the set of all possible output values, or the y-values, that the function can produce. The range represents the vertical extent of the function on the coordinate plane.

Unfortunately, the search results provided do not include specific examples of functions to analyze. However, I can provide you with a general approach to finding the range of a function.

1. Identify the function: Determine the equation or expression that represents the function. For example, if the function is given as y = f(x), identify the expression for f(x).

2. Analyze the function: Depending on the complexity of the function, different methods may be used to find its range. Here are a few common approaches:

- Algebraic manipulation: If the function is a simple algebraic expression, you can manipulate it to find the range. For example, if the function is y = 3x + 2, you can see that the coefficient of x is positive, indicating that the function increases as x increases. Therefore, the range is all real numbers.

- Graphical analysis: Plotting the function on a graph can provide insights into its range. By examining the highest and lowest points on the graph, you can determine the range. For example, if the function is y = sin(x) + cos(x), you can observe that the maximum value of sin(x) + cos(x) is 1 and the minimum value is -1. Therefore, the range of this function is [-1, 1].

- Using calculus: In some cases, calculus techniques such as finding the derivative or critical points can help determine the range. However, this method is more advanced and may not be necessary for simpler functions.

3. Consider any restrictions: Some functions may have restrictions on their domain, which can affect the range. For example, if a function has a denominator that cannot be zero, there will be restrictions on the x-values. These restrictions should be taken into account when determining the range.

It's important to note that without a specific function to analyze, it is difficult to provide a precise answer. If you have a specific function in mind, please provide it, and I'll be happy to help you find its range.