Function domain

[nikonika]

Hello,
I am supposed to determine the domain of this function: f:y=cotg2x/(sin2x+cosx) - in attachments as well, and I have absolutely no idea how to do it or what the result is supposed to be. I have been looking at it for an hour and I am desperate now.
Would anyone be so kind and help me solve it? Maybe describe the solving steps along as well? (English is not my first language, so I apologize ahead for any grammar mistakes).
Thank you very much

 

[Deleted member 4993]

Hello,
I am supposed to determine the domain of this function: f:y=cotg2x/(sin2x+cosx) - in attachments as well, and I have absolutely no idea how to do it or what the result is supposed to be. I have been looking at it for an hour and I am desperate now.
Would anyone be so kind and help me solve it? Maybe describe the solving steps along as well? (English is not my first language, so I apologize ahead for any grammar mistakes).
Thank you very much

Please tell us the definition of the "domain" of a function.

 

[nikonika]

Please tell us the definition of the "domain" of a function.

I think it is also called the defined range? I mean all of the possible values for x.

 

[Deleted member 4993]

I think it is also called the defined range? I mean all of the possible values for x.

So one of the points where the given function is "undefined " would be where the numerator is undefined. What are those point/s?

What else would make f(x) undefined?

 

[nikonika]

So one of the points where the given function is "undefined " would be where the numerator is undefined. What are those point/s?

What else would make f(x) undefined?

I know how to determine the range in simple functions but I don´t know how to do it in this one

 

[BigBeachBanana]

I know how to determine the range in simple functions but I don´t know how to do it in this one

[math]y=\frac{\cot(2x)}{\sin(2x)+\cos(x)}=\frac{\cos(2x)}{\sin(2x)\times (\sin(2x)+\cos(x))}[/math]
Division by 0 leads to an undefined answer, so the function is undefined when:
[math]\sin(2x)=0\\ \sin(2x)+\cos(x)=0[/math]Solve the 2 equations.

 

[Steven G]

sin(2x) + cos(x) = 2sinxcosx +cosx= .......

 

[Deleted member 4993]

sin(2x)=0 .................................(1)

For the equation above (1) , what are the values of 'x' where the equation is satisfied

sin(2x) + cos(x)=0.....................(2)

As Steve showed (response #7)

sin(2x) + cos(x) = 0

2* sin(x) * cos(x) + cos(x) = 0

cos(x) * [2 * sin(x) + 1] = 0 ............................(3)

For the equation above (3) , what are the values of 'x' where the equation is satisfied.