The square root of a negative number is undefined when dealing with real numbers, because the square of any real number is always positive or zero. However, when dealing with complex numbers, the square root of a negative number is defined.
When we consider the square root of -x, where x is a positive real number, the result is the imaginary number i times the square root of x. In this case, the square root of -x is not undefined, but rather a complex number.
For the function f(x) = StartRoot -x EndRoot, the domain is all real numbers, because we can take the square root of any negative number using complex numbers. The range of the function, however, is only imaginary numbers, because the square root of a negative number is always imaginary. This means that the output of the function will never be a real number.
The square root of a negative number, such as StartRoot negative 144 EndRoot, is undefined. Explain why the square root of –x, StartRoot negative x EndRoot, is not necessarily undefined and what this means about the domain and range of f(x) = StartRoot negative x EndRoot.
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