Jenny B. answered • 05/29/19
AP Physics, AP Chemistry, and Math Teacher for 14 Yrs (+Analogies Wiz)
Do you mean f(x) = 2/(3-x)? If so, then the only domain value which would result in a non-real value for y is anything that makes 3-x = 0. In this case, that value is 3. If you try to divide by zero, "infinity" is your answer, which isn't a real number. So if x=3 (this is the domain value), then there is no corresponding real value for the range.
If you in fact meant what you typed, that f(x) = 2/3-x, then there is no domain value which results in a non-real range value. Any real number subtracted from 2/3 will give you another real number.
When working any problem like this, the answer is whatever causes a division by zero or the square root of a negative number.
