What is the domain of tan(x/b)?

[Nope]

Homework Statement

What is the domain for tan(x/b)?

Homework Equations

The Attempt at a Solution

tan(x) domain is all real number , except x=$$\pi/2$$+n pi nEI
tan(x/b)will be bpi/2+bnpi? Is there any form i can write?
Am i right? Thanks

 

[LCKurtz]

Yes. You could write D ={ b(π/2 + nπ) | n ε I}

 

[Nope]

But my teacher said the answer is wrong,
the right answer is bn(pi/2), Can anyone explain it?
Thanks

 

[Mark44]

I think your teacher is wrong. For example, assuming for the moment that b is an integer, if n = 2, 2b*pi/2 = b*pi. tan(2b*pi/2) = tan(b*pi) = 0.

The domain of tan(x) is all reals except odd multiples of pi/2. The tangent function is defined at x = +/-pi, +/-2pi, +/-3pi, etc., but is undefined at x = +/-pi/2, +/-3pi/2, +/-5pi/2.

The graph of y = tan(x/b) is the expansion away from the y-axis of the graph of y = tan(x) by a factor of b, whether or not b is an integer. So tan(x/b) will be undefined at x = +/-b*pi/2, +/-b*3pi/x, +/-b*5pi/x, etc. The domain is all reals except odd multiples of b*pi/2.