Combining functions 

This is a problem from class on Monday, 13 March.

See notes below.

When combining functions, write out the functions to be combined with the appropriate operation between them. Use parentheses when necessary. Simplify.

Remember that the domain of a function is all real numbers, unless there is a limitation on the domain caused by division or taking an even root. If you divide, then the function does not exist where the denominator/divisor is zero. If you take an even root, then the function does not exist where the radicand is negative.

The domain of a combined function cannot be bigger than the domain of either function that went into it. If you are combining two functions, then the limitations on their domains carry over to their combinations.