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- Homework Statement
- The domain of cos is restricted to [0, pi]. What is the implied domain and range of cos(tan^-1(x))?

- Relevant Equations
- y=cos(tan^-1(x))?

Hi everyone

I have the solution to this question, but I'm not sure I understand it.

Why is the domain of the composite function
and not [0, pi]?

Is it because tan^-1 (0 and R+) will always give a value between (-pi/2, pi/2)? I.e. the domain of the composite function refers to x.

Is 0 excluded from the range of the composite function because pi/2 is excluded from the domain of tan^-1?

Thanks

I have the solution to this question, but I'm not sure I understand it.

Why is the domain of the composite function

Is it because tan^-1 (0 and R+) will always give a value between (-pi/2, pi/2)? I.e. the domain of the composite function refers to x.

Is 0 excluded from the range of the composite function because pi/2 is excluded from the domain of tan^-1?

Thanks