The domain of a function is the set of input values for which the function is defined. It is the set of all possible x-values that can be plugged into the function to produce a valid output.
The range of a function is the set of output values that the function can produce for a given set of input values. It is the set of all possible y-values that can be obtained by evaluating the function.
To find the domain of a function, you need to look for any restrictions on the input values. This can include restrictions on the values of x (such as dividing by 0) and restrictions on the type of numbers allowed (such as negative numbers under a radical). The range can be found by looking at the output values that the function can produce.
An inverse function is a function that "undoes" the original function. It switches the input and output values, so that the original output becomes the input and vice versa. For a function to have an inverse, it must pass the horizontal line test, meaning that no two different input values can produce the same output value.
To find the inverse of a function, you can follow these steps:
1. Replace f(x) with y.
2. Switch the x and y variables.
3. Solve for y to get the inverse function.
4. Check that the inverse function passes the horizontal line test.