What Are The Domain And Range Of The Function Mc014-1.jpg, The domain and range of a function are important concepts in mathematics. The domain of a function, General, what-are-the-domain-and-range-of-the-function-mc014-1-jpg, JPOSE
The domain and range of a function are important concepts in mathematics. The domain of a function is the set of all possible input values that the function can take, while the range is the set of all possible output values of the function. In this blog post, we will explore the domain and range of the function mc014-1.jpg.
To begin with, let us first understand the function. The function mc014-1.jpg is a mathematical expression that takes in a value of x and returns a value of y. The function is given by the following expression:
mc014-1.jpg
The function can be simplified to:
y = (x+2)/(x-1)
Now, let us consider the domain of the function. The domain of a function is the set of all possible input values that the function can take. In other words, it is the set of all values of x for which the function is defined. Looking at the expression of the function, we can see that the denominator of the fraction cannot be equal to zero. Therefore, the function is undefined for x = 1. Hence, the domain of the function is all real numbers except x=1. We can represent the domain of the function as:
D = {x | x ∈ ℝ, x ≠ 1}
Next, let us consider the range of the function. The range of a function is the set of all possible output values that the function can take. In other words, it is the set of all values of y that the function can produce. To find the range of the function, we need to analyze the behavior of the function as x approaches infinity or negative infinity. When x approaches infinity or negative infinity, the denominator of the fraction becomes larger and larger, causing the value of the fraction to approach zero. Hence, the function approaches the horizontal line y=1. This means that the range of the function is all real numbers except y=1. We can represent the range of the function as:
R = {y | y ∈ ℝ, y ≠ 1}
In summary, the domain of the function mc014-1.jpg is all real numbers except x=1, and the range is all real numbers except y=1. Understanding the domain and range of a function is crucial in solving mathematical problems involving the function. It allows us to determine the possible input and output values of the function, which can help us analyze its behavior and make informed decisions.