Answer: To find the domain of a curved function, you need to consider the values of x that are allowed in the function. The domain represents all possible x-values for which the function is defined.
Here are the steps to find the domain of a curved function:
1. Identify any restrictions or limitations on the x-values. Look for any values that would cause the function to be undefined, such as dividing by zero or taking the square root of a negative number.
2. Consider the type of function you are dealing with. Different types of functions have different domain restrictions. Here are some common examples:
- Rational functions (those with fractions): Exclude any values of x that would make the denominator equal to zero, as division by zero is undefined.
- Square root functions: The radicand (the expression under the square root symbol) cannot be negative, so exclude any x-values that would result in a negative radicand.
- Logarithmic functions: The argument (the value inside the logarithm) must be positive, so exclude any x-values that would result in a negative or zero argument.
- Trigonometric functions: There are no restrictions on the domain of trigonometric functions, so the domain is typically all real numbers.
3. Combine all the restrictions to determine the final domain of the function. The domain is the set of all x-values that satisfy all the restrictions.
Here's an example to illustrate how to find the domain of a curved function:
Consider the function f(x) = 1/(x-2).
Step 1: There are no restrictions or limitations on x.
Step 2: This function is a rational function, so we need to exclude any x-values that make the denominator (x-2) equal to zero. Solving x-2 = 0 gives x = 2. Therefore, x cannot be equal to 2.
Step 3: Combining the restrictions, the domain of the function f(x) = 1/(x-2) is all real numbers except x = 2.
In summary, to find the domain of a curved function, you need to identify any restrictions on the x-values, consider the type of function, and combine all the restrictions to determine the final domain.
Explanation: