domain of the function

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wendywoo

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Jun 12, 2011
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I can figure out the domain and range easily on a simple equation like x2-1 for example. but i don't know where to start if i have an equation like this one: y=4cscx.
can someone walk me through the steps and teach me how to find the domain of this function??
 
wendywoo said:
I can figure out the domain and range easily on a simple equation like x2-1 for example. but i don't know where to start if i have an equation like this one: y=4cscx.
can someone walk me through the steps and teach me how to find the domain of this function??
Click to expand...

y=cosec(x)

y=1/sin(x)

Domain is all x where Sinx is not equal to zero.
 
wendywoo said:
I can figure out the domain and range easily on a simple equation like x2-1 for example. but i don't know where to start if i have an equation like this one: y=4cscx.
can someone walk me through the steps and teach me how to find the domain of this function??
Click to expand...

I start with plotting the function - where possible.

Then look and eye-ball the answer.

Then figure out - how to prove it.
 
Sin(x)=0 at points where

0+2*k*Pi = x=2*k*Pi

Pi+2*k*Pi=x=Pi*(1+2*k)

k=.....-3,-2,1,0,1,2,3....

so the domain is defined over the points Except where x are defined as so
 
i understand that 1/sinx = cscx but the answer says that the domain x can't be zero or greater than zero. why is that?
 
wendywoo said:
i understand that 1/sinx = cscx but the answer says that the domain x can't be zero or greater than zero. why is that?
Click to expand...

No, as I have proven x - domain can take positive values, too. Say x=Pi/2 radians where x which is greater than zero ( about 1.57 ), right ?

f(Pi/2)=1/1 = 1 where it is definitive

where the range is as

-1<=Sinx<= 1

range ---> ( -infinity, +infinity ) except the (-1,1) interval
 
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