How do I find the domain of the following function algebraically? I can determine it from the graph, but not algebraically.
I don't see a "following function"
To find the domain of a function algebraically, you need to consider any restrictions on the input values. The domain of a function is the set of all possible input values, or the values of x for which the function is defined.
Here are some steps to find the domain of a function algebraically:
1. Identify any expressions or operations in the function that have potential restrictions. Common restrictions include division by zero, taking the square root of a negative number, or any other operations that are undefined for certain values.
2. For division, set the denominator equal to zero and solve for x. If the equation has a solution, exclude that value from the domain because division by zero is undefined.
3. For square roots, logarithms, or other operations with restrictions, set the expression inside the operation greater than or equal to zero, and solve for x. Any values of x that make the expression negative or result in other undefined values should be excluded from the domain.
4. Combine all the values that need to be excluded from the domain, and express the domain as an interval or a combination of intervals.
Keep in mind that different functions may have different restrictions, so it's important to consider the specific algebraic form of the function you are working with. If you provide the function you are trying to find the domain for, I can guide you through the process more specifically.