Maths-
General
Easy

Question

The domain of f left parenthesis x right parenthesis equals fraction numerator 1 over denominator vertical line sin invisible function application x vertical line plus sin invisible function application x end fraction text  is  end text

  1. R
  2. U with n element of Z below left parenthesis left parenthesis 2 n plus 1 right parenthesis pi comma 2 left parenthesis n plus 1 right parenthesis pi right parenthesis
  3. U with n element of Z below left parenthesis 2 n pi comma left parenthesis 2 n plus 1 right parenthesis pi right parenthesis
  4. ϕ

Hint:

in this question, we have to find the domain of f(x). For this denominator must not be equal to 0. Later with the help of range we will get for the sin x will be used to find the domain for f(x).

The correct answer is: U with n element of Z below left parenthesis 2 n pi comma left parenthesis 2 n plus 1 right parenthesis pi right parenthesis


    f left parenthesis x right parenthesis equals fraction numerator 1 over denominator open vertical bar sin space x close vertical bar plus sin space x end fraction
D e n o m i n a t o r not equal to 0
I f space sin space x space greater than 0 comma space space f left parenthesis x right parenthesis space i s space p o s i t i v e.
S o comma space sin space x space plus s i n space x space greater than 0
space space space space space space space space space space space space 2 sin space x space space space space space space space space greater than 0
space space space space space space space space space space space space s i n space x space space space space space space space space space space greater than 0
A s space sin x space greater than space 0 space
S o comma space 2 n straight pi less than straight x less than left parenthesis 2 straight n plus 1 right parenthesis straight pi
So comma space the space d o m a i n space is space U with n element of Z below left parenthesis 2 n pi comma left parenthesis 2 n plus 1 right parenthesis pi right parenthesis.

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