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Mathematics

Functions

Easy

Question

$text If the function end text f colon R minus left curly bracket 1 comma negative 1 right curly bracket not stretchy rightwards arrow A text defined by end text f left parenthesis x right parenthesis equals fraction numerator x squared over denominator 1 minus x squared end fraction comma text end text$ is surjective then A =

$R - [- 1, 0)$
$R - (- 1, 0)$
$R - {- 1}$
$[0, \infty)$

The correct answer is: $R minus left square bracket negative 1 comma 0 right parenthesis$

$text Let end text y equals fraction numerator x squared over denominator 1 minus x squared end fraction. text Then end text y minus y x squared equals x squared not stretchy rightwards double arrow left parenthesis y plus 1 right parenthesis x squared minus y equals 0 x element of R not stretchy rightwards double arrow text Discriminant end text greater or equal than 0 not stretchy rightwards double arrow negative 4 left parenthesis y plus 1 right parenthesis left parenthesis negative y right parenthesis greater or equal than 0 not stretchy rightwards double arrow left parenthesis y plus 1 right parenthesis y greater or equal than 0 not stretchy rightwards double arrow y less or equal than negative 1 text or end text y greater or equal than 0 text If end text y equals negative 1 text then end text fraction numerator x squared over denominator 1 minus x squared end fraction equals negative 1 not stretchy rightwards double arrow x squared equals negative 1 plus x squared text which is not true. end text therefore y less than negative 1 text or end text y greater or equal than 0 not stretchy rightwards double arrow text Range of end text y text is end text R minus left square bracket negative 1 comma 0 right square bracket$

Related Questions to study

$text If end text f colon R not stretchy rightwards arrow A text defined by end text f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x squared plus 2 x plus 2 end fraction straight for all x element of R text is surjective, then end text A equals$

$text If end text f colon R not stretchy rightwards arrow A text defined by end text f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x squared plus 2 x plus 2 end fraction straight for all x element of R text is surjective, then end text A equals$

MathematicsFunctions

If x and {x} represents integral and fractional parts of x,then $left square bracket x right square bracket plus sum from r equals 1 to 2000 of fraction numerator left curly bracket x plus r right curly bracket over denominator 2000 end fraction equals$

If x and {x} represents integral and fractional parts of x,then $left square bracket x right square bracket plus sum from r equals 1 to 2000 of fraction numerator left curly bracket x plus r right curly bracket over denominator 2000 end fraction equals$

MathematicsFunctions

The range of the function $f left parenthesis x right parenthesis equals left square bracket sin x plus cos x right square bracket text (where end text left square bracket x right square bracket$ denotes the greatest integer function is

The range of the function $f left parenthesis x right parenthesis equals left square bracket sin x plus cos x right square bracket text (where end text left square bracket x right square bracket$ denotes the greatest integer function is

MathematicsFunctions

parallel

The range of $square root of vertical line x vertical line minus x end root text is end text$

The range of $square root of vertical line x vertical line minus x end root text is end text$

MathematicsFunctions

If $f left parenthesis x right parenthesis equals fraction numerator sin 3 x over denominator sin x end fraction comma x not equal to n pi$ then the range of f(x) is

If $f left parenthesis x right parenthesis equals fraction numerator sin 3 x over denominator sin x end fraction comma x not equal to n pi$ then the range of f(x) is

MathematicsFunctions

The range of $fraction numerator x squared minus 4 over denominator x minus 2 end fraction text is end text$

The range of $fraction numerator x squared minus 4 over denominator x minus 2 end fraction text is end text$

MathematicsFunctions

parallel

The range of $sec squared x plus 4 cosec squared x$ is

The range of $sec squared x plus 4 cosec squared x$ is

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals a x to the power of 7 plus b x cubed plus c x minus 5 text and end text f left parenthesis negative 7 right parenthesis equals 7$ , then the range of $f left parenthesis 7 right parenthesis plus 17 cos x text is end text$

$text If end text f left parenthesis x right parenthesis equals a x to the power of 7 plus b x cubed plus c x minus 5 text and end text f left parenthesis negative 7 right parenthesis equals 7$ , then the range of $f left parenthesis 7 right parenthesis plus 17 cos x text is end text$

MathematicsFunctions

Domain of $text end text f left parenthesis x right parenthesis equals sin to the power of negative 1 end exponent x plus Sec to the power of negative 1 end exponent x text is end text$

Domain of $text end text f left parenthesis x right parenthesis equals sin to the power of negative 1 end exponent x plus Sec to the power of negative 1 end exponent x text is end text$

MathematicsFunctions

parallel

The domain of the function $f left parenthesis x right parenthesis equals log subscript 3 plus x end subscript open parentheses x squared minus 1 close parentheses text is end text$

The domain of the function $f left parenthesis x right parenthesis equals log subscript 3 plus x end subscript open parentheses x squared minus 1 close parentheses text is end text$

MathematicsFunctions

The domain of $text end text f left parenthesis x right parenthesis equals open parentheses fraction numerator 1 over denominator vertical line x vertical line minus 1 end fraction close parentheses to the power of 1 over 2006 end exponent text is end text$

The domain of $text end text f left parenthesis x right parenthesis equals open parentheses fraction numerator 1 over denominator vertical line x vertical line minus 1 end fraction close parentheses to the power of 1 over 2006 end exponent text is end text$

MathematicsFunctions

The domain of the function f(x) =

The domain of the function f(x) =

MathematicsFunctions

parallel

The domain of $square root of left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end root text is end text$

The domain of $square root of left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end root text is end text$

MathematicsFunctions

The domain of the function f(x) = $fraction numerator 1 over denominator square root of vertical line x vertical line minus x end root end fraction text is : end text$

The domain of the function f(x) = $fraction numerator 1 over denominator square root of vertical line x vertical line minus x end root end fraction text is : end text$

MathematicsFunctions

$text If end text f colon R rightwards arrow R text and end text g colon R rightwards arrow R text are defined by end text f left parenthesis x right parenthesis equals x minus left square bracket x right square bracket text and end text g left parenthesis x right parenthesis equals left square bracket x right square bracket text for end text x element of R text , end text$ where [x] is the greatest integer not exceeding x, $text then for every end text x element of R comma f left parenthesis g left parenthesis x right parenthesis right parenthesis equals$

$text If end text f colon R rightwards arrow R text and end text g colon R rightwards arrow R text are defined by end text f left parenthesis x right parenthesis equals x minus left square bracket x right square bracket text and end text g left parenthesis x right parenthesis equals left square bracket x right square bracket text for end text x element of R text , end text$ where [x] is the greatest integer not exceeding x, $text then for every end text x element of R comma f left parenthesis g left parenthesis x right parenthesis right parenthesis equals$

MathematicsFunctions

parallel

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