Name: Andy

Who is asking: Student

Question:
I'm having difficulty in finding the domain of

1/(x² -2x + 4)

one over x squared minus 2 x plus 4.

I think it is undefined..but my Teacher says it is not. Please help.

It often helps to think of a function as an action of process that takes a number (the input), transforms it somehow, and returns a number (the output). The domain of the function is then the collection of all valid inputs, that is all the numbers that, when input, give a valid real number output. One example is the square root button on a calculator. If you type in a number and then press the square root button you either get a vaild real number output (if you typed in a number greater than or equal to zero) or an error message (if you typed in a negative number.) Thus the domain of the square root function is all numbers which are greater than or equal to zero.

For your function, if you input a number x, the function squares it, subtracts 2 times x and adds 4 to get an intermediate result. The final result is then 1 over this intermediate result. What could go wrong? You can always square a number subtract 2 times the number and add 4 but the next step can give a problem. You know that you can't divide by zero and get a real number, so a problem arises if the intermediate result is zero. Thus the domain is all real numbers except those that make x² -2x + 4 = 0.