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If y = tan^(-1)(x), then the range of y is:
If y = tan^(-1)(x), then the range of y is:
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Practice Questions
1 question
Q1
If y = tan^(-1)(x), then the range of y is:
(-π/2, π/2)
(0, π)
(-π, π)
[0, 1]
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The range of y = tan^(-1)(x) is (-π/2, π/2).
Questions & Step-by-step Solutions
1 item
Q
Q: If y = tan^(-1)(x), then the range of y is:
Solution:
The range of y = tan^(-1)(x) is (-π/2, π/2).
Steps: 5
Show Steps
Step 1: Understand what y = tan^(-1)(x) means. This is the inverse tangent function, which gives the angle whose tangent is x.
Step 2: Recognize that the tangent function can take any real number as input, but its output (the angle) is limited.
Step 3: Know that the tangent function has vertical asymptotes at -π/2 and π/2, meaning it approaches these values but never actually reaches them.
Step 4: Conclude that the output of the inverse tangent function (y) must be between -π/2 and π/2, but not including those values.
Step 5: Therefore, the range of y = tan^(-1)(x) is (-π/2, π/2).
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