I have the following expression:
$$\sqrt[6-x^2]{x}$$
How can I find the values for which this expression if well defined?
I have the following options:
A. $5$ elements
B. $7$ elements
C. an interval
D. $4$ elements
E. no elements
The correct answer is B. $7$ elements, but I don't know how can I arrive at this result.
I shall assume you want the expression to represent only real values here. Then it is equal to $$x^{\frac{1}{6-x^2}}.$$
First, this makes sense only if $x^2\ne 6.$ Secondly, we must have $x>0$ if this is to have a definite real value. Thus, I would say that there is an interval of possible values of $x.$
Perhaps there is a tacit agreement between you and your tester that you only want integer or rational values? That's the only time when a finite number of arguments may be justifiable.