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Maths-

General

Easy

Question

The domain of function, satisfying $f left parenthesis x right parenthesis plus f open parentheses x to the power of negative 1 end exponent close parentheses equals fraction numerator x to the power of 3 end exponent plus 1 over denominator x end fraction$

An empty set
A singleton
A finite set
An infinite set

The correct answer is: A finite set

$f left parenthesis x right parenthesis plus open parentheses fraction numerator 1 over denominator x end fraction close parentheses equals x to the power of 2 end exponent plus fraction numerator 1 over denominator x end fraction$
$text replacing end text rightwards arrow fraction numerator 1 over denominator x end fraction semicolon open parentheses fraction numerator 1 over denominator x end fraction close parentheses minus f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x to the power of 2 end exponent end fraction plus x$
$fraction numerator 1 over denominator x to the power of 2 end exponent end fraction plus x equals x to the power of 2 end exponent plus fraction numerator 1 over denominator x end fraction rightwards double arrow x minus fraction numerator 1 over denominator x end fraction equals x to the power of 2 end exponent minus fraction numerator 1 over denominator x to the power of 2 end exponent end fraction rightwards double arrow open square brackets x minus fraction numerator 1 over denominator x end fraction close square brackets equals open square brackets x minus fraction numerator 1 over denominator x end fraction close square brackets open square brackets x plus fraction numerator 1 over denominator x end fraction close square brackets$
$open square brackets x minus fraction numerator 1 over denominator x end fraction close square brackets open square brackets x plus fraction numerator 1 over denominator x end fraction minus 1 close square brackets equals 0$
$x equals fraction numerator 1 over denominator x end fraction semicolon$
$x plus fraction numerator 1 over denominator x end fraction equals 1 left parenthesis text rejected end text right parenthesis$
$text hence x end text equals 1 text or end text minus 1 rightwards double arrow$
$left curly bracket 1 comma negative 1 rightwards double arrow 3 right curly bracket$

Related Questions to study

The range of the function $f left parenthesis x right parenthesis equals square root of x minus 1 end root plus 2 square root of 3 minus x end root$ is

The range of the function $f left parenthesis x right parenthesis equals square root of x minus 1 end root plus 2 square root of 3 minus x end root$ is

$f colon R rightwards arrow R$ Statement 1 : $f left parenthesis x right parenthesis equals 12 x to the power of 5 end exponent minus 15 x to the power of 4 end exponent plus 20 x to the power of 3 end exponent minus 30 x to the power of 2 end exponent plus 60 x plus 1$ is monotonic and surjective on R because, Statement 2 : A continuous function defined on R, if strictly monotonic has its range R

$f colon R rightwards arrow R$ Statement 1 : $f left parenthesis x right parenthesis equals 12 x to the power of 5 end exponent minus 15 x to the power of 4 end exponent plus 20 x to the power of 3 end exponent minus 30 x to the power of 2 end exponent plus 60 x plus 1$ is monotonic and surjective on R because, Statement 2 : A continuous function defined on R, if strictly monotonic has its range R

Graph of $y equals vertical line 4 x minus 5 vertical line minus$ is

Graph of $y equals vertical line 4 x minus 5 vertical line minus$ is

parallel

If $f left parenthesis x right parenthesis$ and $g left parenthesis x right parenthesis$ are non periodic function then $h left parenthesis x right parenthesis equals f left parenthesis g left parenthesis x right parenthesis right parenthesis$ is

If $f left parenthesis x right parenthesis$ and $g left parenthesis x right parenthesis$ are non periodic function then $h left parenthesis x right parenthesis equals f left parenthesis g left parenthesis x right parenthesis right parenthesis$ is

If $a less or equal than fraction numerator s e c to the power of 2 end exponent invisible function application theta minus t a n invisible function application theta over denominator s e c to the power of 2 end exponent invisible function application theta plus t a n invisible function application theta end fraction less or equal than b$ then a+b=

If $a less or equal than fraction numerator s e c to the power of 2 end exponent invisible function application theta minus t a n invisible function application theta over denominator s e c to the power of 2 end exponent invisible function application theta plus t a n invisible function application theta end fraction less or equal than b$ then a+b=

The set of values of a for which the equation $blank x to the power of 3 end exponent minus 3 x plus a equals 0$ has three distinct real roots is

The set of values of a for which the equation $blank x to the power of 3 end exponent minus 3 x plus a equals 0$ has three distinct real roots is

parallel

Let $text end text alpha text end text$ and $text end text beta text end text$ be the roots of the equation $text end text x to the power of 2 end exponent minus p x plus r equals 0 text end text$ and $text end text fraction numerator alpha over denominator 2 end fraction text , end text blank 2 beta text end text$ be the roots of the equation $x to the power of 2 end exponent minus q x plus r equals 0 text . end text$ The value of $text end text text end text r text end text$ is

Let $text end text alpha text end text$ and $text end text beta text end text$ be the roots of the equation $text end text x to the power of 2 end exponent minus p x plus r equals 0 text end text$ and $text end text fraction numerator alpha over denominator 2 end fraction text , end text blank 2 beta text end text$ be the roots of the equation $x to the power of 2 end exponent minus q x plus r equals 0 text . end text$ The value of $text end text text end text r text end text$ is

The molecules and are

The molecules and are

Chemistry-General

The correct IUPAC name of

The correct IUPAC name of

Chemistry-General

parallel

In which of the compound given below contains more than one kind of hybridization (sp² , sp³ ) for carbon

In which of the compound given below contains more than one kind of hybridization (sp² , sp³ ) for carbon

Chemistry-General

Oxygen as a super oxide is in the form of

Oxygen as a super oxide is in the form of

Chemistry-General

Toluene has

Toluene has

Chemistry-General

parallel

Which of the following statement is not correct?

Which of the following statement is not correct?

Chemistry-General

Which of the following pairs contains mixed oxides ?

Which of the following pairs contains mixed oxides ?

Chemistry-General

S-I : O₃whenever used as oxidising agent essentially liberates O₂
S-II : $3 S n C l subscript 2 end subscript plus 6 H c l plus O subscript 3 end subscript rightwards arrow 3 S n C l subscript 4 end subscript plus 3 H subscript 2 end subscript O$ is possible reaction showing oxidising nature of O_3</sub

S-I : O₃whenever used as oxidising agent essentially liberates O₂
S-II : $3 S n C l subscript 2 end subscript plus 6 H c l plus O subscript 3 end subscript rightwards arrow 3 S n C l subscript 4 end subscript plus 3 H subscript 2 end subscript O$ is possible reaction showing oxidising nature of O_3</sub

Chemistry-General

parallel

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