2
$\begingroup$

When I study the domain my function f:

f[x_] := 2/(Cos[x]^2) + 1/Log[Sin[x]]
FunctionDomain[f[x], x, Reals]

I receive the following answer.

1/2 + x/π ∉ Integers && 
C[1] ∈ Integers && (2 π C[1] < x < 1/2 (π + 4 π C[1]) || 
1/2 (π + 4 π C[1]) < x < π + 2 π C[1])

I find it difficult to interpret the beginning of the answer:

1/2 + x/π ∉ Integers 

Please explain this part. For the rest, I'm ok.

$\endgroup$
1
  • $\begingroup$ @Bendesarts If x had the value of [Pi]/2 the expression 1/2 + x/[Pi] would evaluate to 1, an integer. The expression says that it is prohibited for 1/2 + x/[Pi] to evaluate to be an integer or you will be outside the function domain. $\endgroup$ Nov 7, 2015 at 16:04

1 Answer 1

1
$\begingroup$

Since your f[x] is a sum of two functions, why not try them separately?

FunctionDomain[2/(Cos[x]^2), x, Reals]

1/2 + x/π ∉ Integers

This is saying that values of x for which the denominator is zero are forbidden. The other half is

FunctionDomain[1/Log[Sin[x]], x, Reals]

which gives the rest.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.