What is the range of the function y = tan^(-1)(x)?

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Q: What is the range of the function y = tan^(-1)(x)?

Solution: The range of the function y = tan^(-1)(x) is (-π/2, π/2).

Steps: 6

Step 1: Understand what the function y = tan^(-1)(x) means. This is the inverse tangent function, also known as arctan(x).
Step 2: Know that the output of the arctan function gives you an angle in radians.
Step 3: Recognize that the arctan function takes any real number input (x can be any number).
Step 4: Identify the limits of the output (y) of the arctan function. As x approaches positive infinity, y approaches π/2. As x approaches negative infinity, y approaches -π/2.
Step 5: Conclude that the output (y) never actually reaches -π/2 or π/2, but gets very close to these values.
Step 6: Therefore, the range of the function y = tan^(-1)(x) is all the values between -π/2 and π/2, not including -π/2 and π/2 themselves.