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An Introduction to Functions Video Lecture | Additional Study Material for Class 12
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FAQs on An Introduction to Functions Video Lecture - Additional Study Material for Class 12
| 1. What is a function in mathematics? |  |
A function in mathematics is a relation between a set of inputs (called the domain) and a set of outputs (called the co-domain). It assigns each input a unique output, meaning that for every input there is exactly one output. In other words, a function takes an input value and produces a corresponding output value based on a specific rule or equation.
| 2. How do you represent a function? | |
A function can be represented in various ways. One common way is using a function notation, where the function is denoted by a letter followed by parentheses. For example, f(x) represents a function called "f" with input "x". The function notation allows us to easily distinguish between the function and its variable.
| 3. What is the difference between the domain and co-domain of a function? | |
The domain of a function is the set of all possible input values for the function. It defines the values for which the function is defined and meaningful. On the other hand, the co-domain of a function is the set of all possible output values. It represents the range of values that the function can produce as outputs. It is important to note that not all values in the co-domain may be reached by the function.
| 4. How can you determine if a function is one-to-one? | |
A function is considered one-to-one (or injective) if each input value corresponds to a unique output value. In other words, no two different inputs produce the same output. To determine if a function is one-to-one, we can use the horizontal line test. If any horizontal line intersects the graph of the function at more than one point, then the function is not one-to-one. Additionally, we can analyze the algebraic representation of the function to check for uniqueness in the outputs.
| 5. What is the range of a function? | |
The range of a function represents the set of all possible output values that the function can produce. It is the collection of all the actual output values obtained by evaluating the function for all possible input values in the domain. The range can be determined by analyzing the graph of the function or by examining the outputs of the function for different input values.
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Dec 23, 2024 Last updated |
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