How would you find the domain for f(x) = 2x - 4x^1/2 + 2 ?

Question

How would you find the domain for f(x) = 2x - 4x^1/2 + 2 ? I'm not exactly sure what to do/what steps to take. Do you factor out a 2x^1/2 from the whole problem and then get 2x^1/2 times x²-3x+2?

Answer 1

The domain of this function is all real numbers greater than or equal to zero.  The range is 2 to + infinity.

 

Negative real numbers are excluded from the domain because the square root of a negative number is not real.   The minimum value of the function occurs at x = 0  and has the value 2.   The 2 x term ensures that the upper end of the range is + infinity.