I have to construct a rational function with the range being [-1,0) , which is pretty much just -1.

Wronsonia8g 2022-07-07 Answered
I have to construct a rational function with the range being [-1,0) , which is pretty much just -1. I came up with the solution x 2 1 x . It works for the range, but I'm not sure if it is a rational function.
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Answers (1)

Tanner Hamilton
Answered 2022-07-08 Author has 12 answers
The answer is simply no. A rational function cannot have a square root in their numerator (the denominator of yours is 1). Since your function
f ( x ) = x 2 1 x
has a radical, the function isn't rational (because square roots are not polynomials, so functions with roots are not rational).
Edit:
The term inside the radical isn't a perfect square anyways, since for any value of x, x 2 1 x will never be a perfect square, even for your range of values. Especially for the fact where x=0 because ( 0 ) 2 1 0 cannot be a real root (because the 1 0 part is indeterminate). I credit the commenter of this post for the edit.

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