H(x)= x^x....h(-0.5) is not a real number. Explain why. Please help! I have an exam...and ya, can you please tell me what a real number is with a few examples. Thanks a lot! (the answer sheet said something about square root of a negative number)?

H(x) is defined as x to the power of x. When you try to compute H(-0.5), you find yourself taking -0.5 to the -0.5 power. We recognize that
  (-0.5)^(-0.5)
  = 1/((-0.5)^(0.5))
  = 1/√(-0.5)    (the 1/2 power is the square root)

The square root of a negative number is an imaginary number, not a real number.
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Any number you can write without using "I" is a real number. -√2 is a real number, for example, as is 1, 85, -.354, or any other number you can think of.

H(-0.5) = 1/√(-.5) = 1/(I*√(1/2)) = -I*√2    (the "I" is √-1, signifying an imaginary number)