Inverse trigonometric functions

[Dean54321]

Find the domain, y=cos-1(tanx)

Is the domain and range always classified by the inner function, i.e. tanx?

If so would the domain be -π /2<x<π /2,
and Range: all real y.

Finally, I'm extremely unsure how to graph it, is it meant to resemble the cos-1 curve?

All help is appreciated thank you.

 

[Dr.Peterson]

Find the domain, y=cos-1(tanx)

Is the domain and range always classified by the inner function, i.e. tanx?

If so would the domain be -π /2<x<π /2,
and Range: all real y.

Finally, I'm extremely unsure how to graph it, is it meant to resemble the cos-1 curve?

All help is appreciated thank you.

Both functions play a role in the domain and range of the composite function.

In addition to x needing to be in the domain of the inner function, the output of that function has to be in the domain of the outer function. Observe that tan(x) is not always in [-1, 1], the domain of cos^-1. For what values of x will it be in that interval?

If you were told to graph the composite function, I would first try to simplify it. I don't think that can be done here. I see no evidence here that you are expected to.

To find the range, find the inverse.