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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: $R minus left square bracket negative 1 comma 0 right parenthesis$

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

Related Questions to study

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

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

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals fraction numerator a to the power of x minus 1 over denominator x to the power of n open parentheses a to the power of x plus 1 close parentheses end fraction$ is even then n =

$text If end text f left parenthesis x right parenthesis equals fraction numerator a to the power of x minus 1 over denominator x to the power of n open parentheses a to the power of x plus 1 close parentheses end fraction$ is even then n =

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Among the following functions defined on R into R, the constant function is

Among the following functions defined on R into R, the constant function is

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parallel

$text Let end text f left parenthesis x right parenthesis equals fraction numerator x over denominator e to the power of x minus 1 end fraction plus x over 2 plus 1 comma text then end text f text is end text$

$text Let end text f left parenthesis x right parenthesis equals fraction numerator x over denominator e to the power of x minus 1 end fraction plus x over 2 plus 1 comma text then end text f text is end text$

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals fraction numerator 2 x left parenthesis sin x plus tan x right parenthesis over denominator 2 open square brackets fraction numerator x plus 21 pi over denominator pi end fraction close square brackets minus 41 end fraction comma x not equal to n pi comma text end text$ then f is

$text If end text f left parenthesis x right parenthesis equals fraction numerator 2 x left parenthesis sin x plus tan x right parenthesis over denominator 2 open square brackets fraction numerator x plus 21 pi over denominator pi end fraction close square brackets minus 41 end fraction comma x not equal to n pi comma text end text$ then f is

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals fraction numerator cos x sin x over denominator tan x plus cot x end fraction text end text$ then function f(x) is

$text If end text f left parenthesis x right parenthesis equals fraction numerator cos x sin x over denominator tan x plus cot x end fraction text end text$ then function f(x) is

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The function $text end text f left parenthesis x right parenthesis equals log open parentheses x plus square root of x squared plus 1 end root close parentheses text is end text$

The function $text end text f left parenthesis x right parenthesis equals log open parentheses x plus square root of x squared plus 1 end root close parentheses text is end text$

MathematicsFunctions

$text Let end text g colon R not stretchy rightwards arrow open parentheses 0 comma pi over 3 close square brackets text be defined by end text g left parenthesis x right parenthesis equals cos to the power of negative 1 end exponent open parentheses fraction numerator x squared minus k over denominator 1 plus x squared end fraction close parentheses space$ Then find the possible values of k for which g is surjective function

$text Let end text g colon R not stretchy rightwards arrow open parentheses 0 comma pi over 3 close square brackets text be defined by end text g left parenthesis x right parenthesis equals cos to the power of negative 1 end exponent open parentheses fraction numerator x squared minus k over denominator 1 plus x squared end fraction close parentheses space$ Then find the possible values of k for which g is surjective function

MathematicsFunctions

$text If end text f colon N not stretchy rightwards arrow Z space f left parenthesis n right parenthesis equals open curly brackets table attributes columnalign left columnspacing 1em end attributes row cell fraction numerator n minus 1 over denominator 2 end fraction comma text when end text n text is odd end text end cell row cell negative n over 2 comma text when end text n text is even end text end cell end table close$ Identify the type of function

$text If end text f colon N not stretchy rightwards arrow Z space f left parenthesis n right parenthesis equals open curly brackets table attributes columnalign left columnspacing 1em end attributes row cell fraction numerator n minus 1 over denominator 2 end fraction comma text when end text n text is odd end text end cell row cell negative n over 2 comma text when end text n text is even end text end cell end table close$ Identify the type of function

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parallel

Which of the following functions from Z to it self are bijections?

Which of the following functions from Z to it self are bijections?

MathematicsFunctions

Let f(x) be a function and k be a positive real number such that
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Let f(x) be a function and k be a positive real number such that
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MathematicsFunctions

If f(x) is polynomial function satisfying $text end text f left parenthesis x right parenthesis times f open parentheses 1 over x close parentheses equals f left parenthesis x right parenthesis plus f open parentheses 1 over x close parentheses text and end text text end text f left parenthesis 4 right parenthesis equals 65 comma text then find end text f left parenthesis 6 right parenthesis$

If f(x) is polynomial function satisfying $text end text f left parenthesis x right parenthesis times f open parentheses 1 over x close parentheses equals f left parenthesis x right parenthesis plus f open parentheses 1 over x close parentheses text and end text text end text f left parenthesis 4 right parenthesis equals 65 comma text then find end text f left parenthesis 6 right parenthesis$

MathematicsFunctions

parallel

Let f be a function satisfying f(xy) = $fraction numerator f left parenthesis x right parenthesis over denominator y end fraction$ for all positive real numbers x and y if f(30) =20, then find the value of f(40)

Let f be a function satisfying f(xy) = $fraction numerator f left parenthesis x right parenthesis over denominator y end fraction$ for all positive real numbers x and y if f(30) =20, then find the value of f(40)

MathematicsFunctions

$text Let a function end text f left parenthesis x right parenthesis text satisfies end text f left parenthesis x right parenthesis plus f left parenthesis 2 x right parenthesis plus f left parenthesis 2 minus x right parenthesis plus f left parenthesis 1 plus x right parenthesis equals x straight for all x element of R.$ Then find the value of f(0)

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MathematicsFunctions

The function f(x) is defined for all real x. If f(a+b) =f(ab) $for all a text and end text b$ $text and end text f open parentheses negative 1 half close parentheses equals negative 1 half$ then find the value of f(1005)

The function f(x) is defined for all real x. If f(a+b) =f(ab) $for all a text and end text b$ $text and end text f open parentheses negative 1 half close parentheses equals negative 1 half$ then find the value of f(1005)

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