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Example Question #10 : Graphing Inverse Trig Functions
State the domain and range of and
.
domain:
range:
domain:
range:
domain:
range:
domain:
range:
, such that
domain:
range:
domain:
range:
domain:
range:
domain:
range:
domain:
, such that
range:
domain:
range:
domain:
, such that
range:
domain:
range:
The two graphs help provide a visual. The domain is all possible x values, and the range is all possible y values. The arctan function exchanges all x and y values of the tangent function. However, in order to continue being a function (by passing the horizontal line test), the arctangent function's range is restricted to . It is not a coincidence that the range of the tangent function is equal to the domain of the arctangent function because of the nature of inverse relationships.
domain:
, such that
range:
domain:
range:
You can see that while the range and the
domain match, the
domain and the
range are not exact matches; this is so that
can be a function (by being restricted).
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