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Maths-

General

Easy

Question

The domain of the function $f left parenthesis x right parenthesis equals fraction numerator tan invisible function application 2 x over denominator 6 cos invisible function application x plus 2 sin invisible function application 2 x end fraction text is end text$

$R - \{(2 n + 1) \frac{π}{2} : n \in Z\}$
$R - \{(2 n + 1) \frac{π}{4} : n \in Z\}$
$R - \{(2 n + 1) \frac{π}{2} : n \in Z\}$
$R - \{(2 n + 1) \frac{π}{4} : n \in Z\}$

hint Hint:

in this question, we have to find the domain of f(x). First considering the numerator and finding its domain and later considering the denominator and finding its domain. Further, find the total domains that satisfy the equation.

The correct answer is: $R minus open curly brackets left parenthesis 2 n plus 1 right parenthesis pi over 2 colon n element of Z close curly brackets$

$f left parenthesis x right parenthesis equals fraction numerator tan space 2 x over denominator 6 cos space x plus 2 space sin space 2 x space end fraction A s space tan space i s space u n d e f i n e d space a t space o d d space i n t e g r a l space m u l t i p l e space o f straight pi over 2. 2 x space not equal to space straight pi over 2 left parenthesis 2 straight n plus 1 right parenthesis straight x space space not equal to fraction numerator straight pi left parenthesis 2 straight n plus 1 right parenthesis over denominator 4 end fraction Now comma space for space denominator comma space 6 cos space straight x space plus 2 space sin 2 straight x space not equal to 0 6 space cos space straight x space plus 2.2 space sin space straight x space cos space straight x space not equal to 0 2 space cos space straight x left parenthesis 3 plus 2 sin space straight x right parenthesis not equal to 0 2 space cos space straight x space not equal to 0 space space space space 0 straight r space 3 plus 2 sin space straight x space not equal to 0 For comma 2 space cos space straight x space not equal to 0 rightwards double arrow cos space straight x not equal to 0 For comma space 3 plus 2 sin space straight x not equal to 0 rightwards double arrow 2 sin space straight x not equal to negative 3 rightwards double arrow sinx space not equal to fraction numerator negative 3 over denominator 2 end fraction minimum space value space of space sin space straight x space is space minus 1 space. cos space not equal to 0 comma space cos space is space 0 space at space odd space integral space multiple space of space straight pi over 2. so comma space straight x not equal to fraction numerator left parenthesis 2 straight n plus 1 right parenthesis straight pi over denominator 2 end fraction so comma d o m a i n space o f space f left parenthesis x right parenthesis space i s space R minus open curly brackets left parenthesis 2 n plus 1 right parenthesis pi over 2 colon n element of Z close curly brackets$

Related Questions to study

Let $f colon open square brackets 1 half comma 1 close square brackets not stretchy rightwards arrow left square bracket negative 1 comma 1 right square bracket$ is given by $f left parenthesis x right parenthesis equals 4 x cubed minus 3 x text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis text is given by end text$

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If $f left parenthesis x right parenthesis equals x squared plus x comma x equals 10 comma delta x equals 0.1$ observe the following
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$text II) end text d f equals 2.1$
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The true statements are

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$text l) end text delta f equals 2.11$
$text II) end text d f equals 2.1$
$text III) Relative error in end text x text is end text 1$
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