Domain of a function

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  • #1
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Homework Statement


let f(x) = sqrt(1-sin(x))


Homework Equations


What is the domain of f?
What is the domain of f'(x)?


The Attempt at a Solution


I understand that the domain of f is all real numbers not including every increment of 90 degrees, but im not sure how to state that.
I also found that f'(x) = (1/2 -sin(x))(-cos(x)) im not sure if thats correct though
 

Answers and Replies

  • #2
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A point is not in the domain if it does not have a function value. The only possible situation that [tex] f(x)=\sqrt{1-sin(x)} [/tex] does not exist, is when you take the root of a negative number. So you will have to search for what x we have that 1-sin(x)<0.
 
  • #3
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go on google and type

wolfrom alpha

look at the graphs and try understand
 
  • #4
hunt_mat
Homework Helper
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Micromass is spot on here, for what values of x satisfy [tex]\sin x\leqslant 1[/tex]? Do you know the graph of [tex]\sin x[/tex]?
 
  • #5
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so the domain is all real numbers except when sin(x)<1?
 
  • #6
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Yes! But can you say explicitly when sin(x)<1?
 
  • #7
hunt_mat
Homework Helper
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No that's not what we're saying the domain if all numbers which satisfy sin(x)<1, not the other way around.
 
  • #8
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thats where i got lost
 

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