Domain of Functions

Question

How do I figure these out?

What is the domain of each function

1. f(x) = 3x²/x²-1

1. f(x) = 1/x-1

1. f(x) = x²+ x - 20 / x² + 8x + 16

Answer 1

So the domain of the function is all possible values that your independent variable can take, in this case, the x variable. Generally speaking, when dealing with algebraic functions, the domain will typically be all real numbers (neg inf - pos inf). Only on the case where your independent variable is restricted will this change. A good thing to look for are expressions that contain the independent variable (usually x) under a radical (sq. root, for example) as the expression under the sq root cannot be negative. Another thing to look for is rational expressions, expressions that involve dividing two or more seperate expressions, as are in your problems. In these cases, if the denominator contains the independent variable, then you will need to find the value(s) of the variable that make the denominator 0 because you cannot divide by 0. A denominator of 0 makes the function undefined and that value will not be in your domain. Hope this was helpful!