document.write( "Question 1209617: Suppose the domain of f is (-1,3). Define the function g by
\n" ); document.write( "g(x) = f(sqrt(x)/sqrt(-x)).
\n" ); document.write( "What is the domain of g? \n" ); document.write( "
Algebra.Com's Answer #849704 by CPhill(1987)\"\" \"About 
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Here's how to determine the domain of g:\r
\n" ); document.write( "\n" ); document.write( "1. **Analyze the input to f:**\r
\n" ); document.write( "\n" ); document.write( "The function g(x) is defined as g(x) = f(√(x)/√(-x)). The input to the function f is the expression √(x)/√(-x).\r
\n" ); document.write( "\n" ); document.write( "2. **Consider the square roots:**\r
\n" ); document.write( "\n" ); document.write( "For √(x) to be defined, x must be greater than or equal to 0 (x ≥ 0).
\n" ); document.write( "For √(-x) to be defined, -x must be greater than or equal to 0, which means x must be less than or equal to 0 (x ≤ 0).\r
\n" ); document.write( "\n" ); document.write( "3. **Combine the restrictions:**\r
\n" ); document.write( "\n" ); document.write( "The expression √(x)/√(-x) requires *both* x ≥ 0 and x ≤ 0 to be true. The only value that satisfies both conditions is x = 0.\r
\n" ); document.write( "\n" ); document.write( "4. **Evaluate the expression at x = 0:**\r
\n" ); document.write( "\n" ); document.write( "When x = 0, the expression becomes √(0)/√(-0) = 0/0, which is undefined.\r
\n" ); document.write( "\n" ); document.write( "5. **Consider the domain of f:**\r
\n" ); document.write( "\n" ); document.write( "Even if the expression √(x)/√(-x) were defined, its value would need to fall within the domain of f, which is (-1, 3).\r
\n" ); document.write( "\n" ); document.write( "6. **Determine the domain of g:**\r
\n" ); document.write( "\n" ); document.write( "Since the expression √(x)/√(-x) is undefined for all x, the function g(x) is also undefined for all x. Therefore, the domain of g is the empty set, often represented as {}.
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