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Mathematics

Functions

Easy

Question

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

An odd function
An even function
Periodic function
None of these

The correct answer is: An even function

$f left parenthesis negative x right parenthesis equals fraction numerator negative x over denominator e to the power of negative x end exponent minus 1 end fraction minus x over 2 plus 1 equals fraction numerator negative x e to the power of x over denominator 1 minus e to the power of x end fraction minus x over 2 plus 1 equals fraction numerator x e to the power of x over denominator e to the power of x minus 1 end fraction minus x over 2 plus 1 equals fraction numerator x open parentheses e to the power of x minus 1 close parentheses plus x over denominator e to the power of x minus 1 end fraction minus x over 2 plus 1 equals fraction numerator x over denominator e to the power of x minus 1 end fraction plus x over 2 plus 1 equals f left parenthesis x right parenthesis therefore f text is an even function. end text$

Related Questions to study

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

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

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

MathematicsFunctions

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

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

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

MathematicsFunctions

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

MathematicsFunctions

parallel

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

MathematicsFunctions

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

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

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

parallel

$text If end text f left parenthesis x right parenthesis equals fraction numerator cos x sin x over denominator tan x plus cot x end fraction text end text$ 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

MathematicsFunctions

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

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

MathematicsFunctions

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
$f left parenthesis x plus k right parenthesis plus f left parenthesis x right parenthesis equals 0 space f o r space a l l space x element of R. space t h e n space f i n d space t h e space p e r i o d space o f space f left parenthesis x right parenthesis space$

Let f(x) be a function and k be a positive real number such that
$f left parenthesis x plus k right parenthesis plus f left parenthesis x right parenthesis equals 0 space f o r space a l l space x element of R. space t h e n space f i n d space t h e space p e r i o d space o f space f left parenthesis x right parenthesis space$

MathematicsFunctions

parallel

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