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The **Domain Calculator** is a powerful tool that allows you to easily calculate the domain of any type of single-variable function. With just a few simple steps, you can determine the set of values that a function can accept as input.

To use the Domain Calculator, simply follow these three easy steps:

- Enter the function for which you want to calculate the domain.
- Select the independent variable that will be taken into account for the calculation.
- Press the green “Calculate” button. When you press this button, the solution will automatically appear.

With the Domain Calculator at your fingertips, you’ll be able to quickly and accurately calculate the domain of any function, saving you time and effort in your studies or work. Try it out today and see the power of this tool for yourself!

Valid functions and symbols | Description |
---|---|

sqrt() | Square root |

ln(), log() | Natural logarithm |

log10() | Logarithm base 10 |

^ | Exponents |

abs() | Absolute value |

sin(), cos(), tan(), csc(), sec(), cot() | Basic trigonometric functions |

asin(), acos(), atan(), acsc(), asec(), acot() | Inverse trigonometric functions |

sinh(), cosh(), tanh(), csch(), sech(), coth() | Hyperbolic functions |

asinh(), acosh(), atanh(), acsch(), asech(), acoth() | Inverse hyperbolic functions |

pi | PI number (π = 3.14159…) |

e | Neper number (e= 2.71828…) |

i | To indicate the imaginary component of a complex number. |

u() | Heaviside step function |

The domain of a function is the set of values that the function can accept as input. In other words, it is the set of values for which the function is defined. For example, if the function is f(x) = x^{2}, the domain of the function is all real numbers, since the function is defined for all values of x. On the other hand, if the function is g(x) = 1/x, the domain of the function is all real numbers except x = 0, since the function is not defined for x = 0.

It’s important to note that the domain of a function can be a finite set of values, an infinite set of values, or a combination of both. It’s also possible for the domain of a function to be restricted in certain ways, for example by specifying that the input values must be greater than or equal to a certain number.

In order to determine the domain of a function, you can use the rules of algebra and the properties of the specific mathematical operations used in the function. You can also use a tool such as the Domain Calculator to quickly and accurately calculate the domain of a function.

To find the domain of a function, you can use the following steps:

- Identify any restrictions on the input values, such as conditions that the input must be greater than or equal to a certain number.
- Determine which values of the input would result in the function being undefined, such as division by zero or the square root of a negative number.
- Use the rules of algebra and the properties of the specific mathematical operations used in the function to determine which values of the input are allowed.

Here’s an example to illustrate the process:

Consider the function *f*(*x*) = *x*−3*x*^{2}+2*x*−3 . To find the domain of this function, we can follow these steps:

- Write down the function:
*f*(*x*) =*x*−3*x*^{2}+2*x*−3 - There are no restrictions on the input values specified in this function.
- The function is undefined when the denominator is equal to zero, so we need to find the values of x that make the denominator equal to zero. To do this, we can set the denominator equal to zero and solve for x:
*x*^{2}+2*x*−3 = 0. Using the quadratic formula, we find that the solutions are x = -3 and x = 1. - The function is defined for all values of x except x = -3 and x = 1. Therefore, the domain of the function is all real numbers except -3 and 1.

In this case, the domain of the function is a finite set of values: all real numbers except -3 and 1.

D{f(x)}= {*x*∈ℝ: *x* ≠ −3 ; *x* ≠ 1}