Function
A function is a mathematical relationship between two sets of values, known as the domain and the range
A function is a mathematical relationship between two sets of values, known as the domain and the range. It takes input values from the domain and assigns unique output values in the range. In other words, for every input, there is exactly one output.
A function is typically represented by f(x) or y = f(x), where “x” is the input and “f(x)” or “y” is the output. The input values can be numbers, variables, or even objects like vectors. The output values depend on the specific definition of the function.
For example, consider the function f(x) = 2x + 3. This function takes any number x as input, multiplies it by 2, and then adds 3. The output, or value of f(x), is the result of this calculation.
To find the value of f(x) for a specific input, you substitute the value of x into the function and perform the required operation. For instance, if we want to know f(4), we substitute 4 for x in the function:
f(4) = 2(4) + 3 = 8 + 3 = 11
Therefore, f(4) = 11.
Functions can have different properties, such as being linear, quadratic, exponential, or trigonometric. They can also be defined by formulas, graphs, or tables of values.
It’s important to note that functions must satisfy the criteria of assigning a unique output to each input. If a single input value has more than one corresponding output value, then it is not a function.
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