Video Transcript
Determine the domain and range of the function ๐ of ๐ฅ equals one over ๐ฅ minus two.
We have this function ๐ of ๐ฅ equals one over ๐ฅ minus two, but we donโt have a graph. Is there a way we can solve this algebraically? Can we solve this without graphing? Actually, we can. Something that we know about division is that we canโt divide something by zero. And that means that any time whatโs in the denominator would be equal to zero. Itโs not a possibility for this function.
If we set ๐ฅ minus two equal to zero and solve, we get ๐ฅ equal to two. Our function would not have a solution at ๐ฅ equal to two. This is the only place for our ๐ฅ-values that this equation would not work. Because of that, we can say that our domain is all real numbers with the exception or minus two.
Something else interesting happens when we deal with these kinds of inverse functions. Our ๐ of ๐ฅ cannot be equal to zero. No matter what we put in the denominator, weโll never divide one by something and equal zero. Itโs impossible. So we say that our range is all real numbers with the exception of zero โ all reals minus zero.