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Question

Number of solutions of the equation $tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 2 x plus 1 end fraction close parentheses plus tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 4 x plus 1 end fraction close parentheses equals tan to the power of negative 1 end exponent invisible function application open parentheses 2 over x squared close parentheses$ is

1
2
3
4

The correct answer is: 2

Given,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 2 x plus 1 end fraction close parentheses plus tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 4 x plus 1 end fraction close parentheses end cell row cell equals tan to the power of negative 1 end exponent invisible function application open parentheses 2 over x squared close parentheses end cell row cell not stretchy rightwards double arrow tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator fraction numerator 1 over denominator 2 x plus 1 end fraction plus fraction numerator 1 over denominator 4 x plus 1 end fraction over denominator 1 minus fraction numerator 1 over denominator 2 x plus 1 end fraction cross times fraction numerator 1 over denominator 4 x plus 1 end fraction end fraction close parentheses end cell row cell not stretchy rightwards double arrow tan to the power of negative 1 end exponent invisible function application open parentheses 2 over x squared close parentheses end cell row cell not stretchy rightwards double arrow tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 6 x plus 2 over denominator 8 x squared plus 6 x end fraction close parentheses equals tan to the power of negative 1 end exponent invisible function application open parentheses 2 over x squared close parentheses end cell end table$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 6 x cubed plus 2 x squared equals 16 x squared plus 12 x end cell row cell not stretchy rightwards double arrow 6 x cubed minus 14 x squared minus 12 x equals 0 end cell row cell not stretchy rightwards double arrow 2 x open parentheses 3 x squared minus 7 x minus 6 close parentheses equals 0 end cell row cell not stretchy rightwards double arrow 2 x left parenthesis 3 x plus 2 right parenthesis left parenthesis x minus 3 right parenthesis equals 0 end cell row cell not stretchy rightwards double arrow x equals 0 comma negative 2 over 3 comma 3 end cell end table$
But $x equals negative 2 over 3$ does not satisfy the given relation

Related Questions to study

$text If end text sec to the power of negative 1 end exponent invisible function application square root of 1 plus x squared end root plus cosec to the power of negative 1 end exponent invisible function application fraction numerator square root of 1 plus y squared end root over denominator y end fraction plus cot to the power of negative 1 end exponent invisible function application 1 over z equals pi$ $text then end text x plus y plus z$ is equal to

$text If end text sec to the power of negative 1 end exponent invisible function application square root of 1 plus x squared end root plus cosec to the power of negative 1 end exponent invisible function application fraction numerator square root of 1 plus y squared end root over denominator y end fraction plus cot to the power of negative 1 end exponent invisible function application 1 over z equals pi$ $text then end text x plus y plus z$ is equal to

$cos invisible function application open square brackets cos to the power of negative 1 end exponent invisible function application open parentheses negative 1 over 7 close parentheses plus sin to the power of negative 1 end exponent invisible function application open parentheses negative 1 over 7 close parentheses close square brackets text is equal to end text$

$cos invisible function application open square brackets cos to the power of negative 1 end exponent invisible function application open parentheses negative 1 over 7 close parentheses plus sin to the power of negative 1 end exponent invisible function application open parentheses negative 1 over 7 close parentheses close square brackets text is equal to end text$

$tan to the power of negative 1 end exponent invisible function application fraction numerator x over denominator square root of a squared minus x squared end root end fraction$ is equal to

$tan to the power of negative 1 end exponent invisible function application fraction numerator x over denominator square root of a squared minus x squared end root end fraction$ is equal to

parallel

If $theta equals sin to the power of negative 1 end exponent invisible function application x plus cos to the power of negative 1 end exponent invisible function application x minus tan to the power of negative 1 end exponent invisible function application x comma 1 less or equal than x less than straight infinity$ , then the smallest interval in which θ lies is

If $theta equals sin to the power of negative 1 end exponent invisible function application x plus cos to the power of negative 1 end exponent invisible function application x minus tan to the power of negative 1 end exponent invisible function application x comma 1 less or equal than x less than straight infinity$ , then the smallest interval in which θ lies is

If $A equals open square brackets table attributes columnalign center center center center columnspacing 1em end attributes row cell cos squared end cell alpha cell cos invisible function application horizontal ellipsis horizontal ellipsis end cell cell alpha sin invisible function application horizontal ellipsis horizontal ellipsis end cell row cell cos invisible function application horizontal ellipsis end cell cell alpha sin end cell alpha cell sin squared invisible function application alpha end cell end table close square brackets$ and $A equals open square brackets table attributes columnalign center center center center columnspacing 1em end attributes row cell cos squared end cell beta cell cos invisible function application horizontal ellipsis sin end cell alpha row cos cell beta sin end cell cell sin squared invisible function application beta end cell beta end table close square brackets$ are two matrices such that the product AB is null matrix, then $alpha minus beta$ is

If $A equals open square brackets table attributes columnalign center center center center columnspacing 1em end attributes row cell cos squared end cell alpha cell cos invisible function application horizontal ellipsis horizontal ellipsis end cell cell alpha sin invisible function application horizontal ellipsis horizontal ellipsis end cell row cell cos invisible function application horizontal ellipsis end cell cell alpha sin end cell alpha cell sin squared invisible function application alpha end cell end table close square brackets$ and $A equals open square brackets table attributes columnalign center center center center columnspacing 1em end attributes row cell cos squared end cell beta cell cos invisible function application horizontal ellipsis sin end cell alpha row cos cell beta sin end cell cell sin squared invisible function application beta end cell beta end table close square brackets$ are two matrices such that the product AB is null matrix, then $alpha minus beta$ is

If $A equals left square bracket x y z right square bracket comma B equals open square brackets table attributes columnspacing 1em end attributes row cell a straight h invisible function application g end cell row cell h b f end cell row cell g f c end cell end table close square brackets$ and $C equals open square brackets table attributes columnalign left columnspacing 1em end attributes row x row y row z end table close square brackets$ Then, $B to the power of straight prime left parenthesis A B right parenthesis equals 0$ if

If $A equals left square bracket x y z right square bracket comma B equals open square brackets table attributes columnspacing 1em end attributes row cell a straight h invisible function application g end cell row cell h b f end cell row cell g f c end cell end table close square brackets$ and $C equals open square brackets table attributes columnalign left columnspacing 1em end attributes row x row y row z end table close square brackets$ Then, $B to the power of straight prime left parenthesis A B right parenthesis equals 0$ if

parallel

The function $f colon R not stretchy rightwards arrow R$ given by $f left parenthesis x right parenthesis equals x cubed minus 1$ is

The function $f colon R not stretchy rightwards arrow R$ given by $f left parenthesis x right parenthesis equals x cubed minus 1$ is

$f left parenthesis x right parenthesis equals x plus square root of x squared end root$ is a function from R to R, then $f left parenthesis x right parenthesis$ is

$f left parenthesis x right parenthesis equals x plus square root of x squared end root$ is a function from R to R, then $f left parenthesis x right parenthesis$ is

Which of the following functions is one-to -one?

Which of the following functions is one-to -one?

parallel

A mapping $f colon N not stretchy rightwards arrow N$ , where N is the set of natural numbers is defined as $f left parenthesis n right parenthesis equals open curly brackets table attributes columnspacing 1em end attributes row cell n squared comma text for end text n text odd end text end cell row cell 2 n plus 1 comma text for end text n text even end text end cell end table close$ For $n element of N$ Then, $f$ is

A mapping $f colon N not stretchy rightwards arrow N$ , where N is the set of natural numbers is defined as $f left parenthesis n right parenthesis equals open curly brackets table attributes columnspacing 1em end attributes row cell n squared comma text for end text n text odd end text end cell row cell 2 n plus 1 comma text for end text n text even end text end cell end table close$ For $n element of N$ Then, $f$ is

Let $A equals R minus left curly bracket 3 right curly bracket comma B equals R minus left curly bracket 1 right curly bracket text Let end text f colon A not stretchy rightwards arrow B$ be defined by $f left parenthesis x right parenthesis equals fraction numerator x minus 2 over denominator x minus 3 end fraction$ .Then,

Let $A equals R minus left curly bracket 3 right curly bracket comma B equals R minus left curly bracket 1 right curly bracket text Let end text f colon A not stretchy rightwards arrow B$ be defined by $f left parenthesis x right parenthesis equals fraction numerator x minus 2 over denominator x minus 3 end fraction$ .Then,

The mapping $f colon N not stretchy rightwards arrow N$ given $f left parenthesis n right parenthesis equals 1 plus n squared comma n element of N$ where N is the set of natural number, is

The mapping $f colon N not stretchy rightwards arrow N$ given $f left parenthesis n right parenthesis equals 1 plus n squared comma n element of N$ where N is the set of natural number, is

parallel

The function $f colon R not stretchy rightwards arrow R$ defined by $f left parenthesis x right parenthesis equals left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis$ is

The function $f colon R not stretchy rightwards arrow R$ defined by $f left parenthesis x right parenthesis equals left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis$ is

Let A be a set containing 10 distinct elements, then the total number of distinct function from A to A is

Let A be a set containing 10 distinct elements, then the total number of distinct function from A to A is

$A equals left curly bracket 1 comma 2 comma 3 comma 4 right curly bracket comma B left curly bracket 1 comma 2 comma 3 comma 4 comma 5 comma 6 right curly bracket$ are two sets, and function $f colon A not stretchy rightwards arrow B$ is defined by $f left parenthesis x right parenthesis equals x plus 2 straight for all x element of A$ , then the function $f$ is

$A equals left curly bracket 1 comma 2 comma 3 comma 4 right curly bracket comma B left curly bracket 1 comma 2 comma 3 comma 4 comma 5 comma 6 right curly bracket$ are two sets, and function $f colon A not stretchy rightwards arrow B$ is defined by $f left parenthesis x right parenthesis equals x plus 2 straight for all x element of A$ , then the function $f$ is

parallel

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