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Mathematics

Functions

Easy

Question

If [ ] denotes the greatest integer function and if $f colon left parenthesis 5 comma 10 right parenthesis rightwards arrow left parenthesis 7 comma 12 right parenthesis$ is a function defined by $f left parenthesis x right parenthesis equals x plus 2 open square brackets x over 5 close square brackets text , then end text$

$f^{- 1} (x) = x - 1$
$f^{- 1} (x) = x + 2$
$f^{- 1} (x) = x - 2$
$f^{- 1} (x) does not exist$

The correct answer is: $f to the power of negative 1 end exponent left parenthesis x right parenthesis equals x minus 2$

$text Given end text f colon left parenthesis 5 comma 10 right parenthesis not stretchy rightwards arrow left parenthesis 7 comma 12 right parenthesis text defined by end text f left parenthesis x right parenthesis equals x plus 2 open square brackets x over 5 close square brackets text Here end text 5 less than x less than 10 not stretchy rightwards double arrow 1 less than x over 5 less than z not stretchy rightwards double arrow open square brackets x over 5 close square brackets equals 1 not stretchy rightwards double arrow f left parenthesis x right parenthesis equals x plus 2 text Let end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals y not stretchy rightwards double arrow x equals f left parenthesis y right parenthesis not stretchy rightwards double arrow x equals y plus 2 not stretchy rightwards double arrow y equals x minus 2 not stretchy rightwards double arrow f to the power of negative 1 end exponent left parenthesis x right parenthesis equals x minus 2$

Related Questions to study

$text If end text f colon left square bracket 1 comma straight infinity right parenthesis not stretchy rightwards arrow left square bracket 2 comma straight infinity right parenthesis text is given by end text f left parenthesis x right parenthesis equals x plus 1 over x text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

$text If end text f colon left square bracket 1 comma straight infinity right parenthesis not stretchy rightwards arrow left square bracket 2 comma straight infinity right parenthesis text is given by end text f left parenthesis x right parenthesis equals x plus 1 over x text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

MathematicsFunctions

$text If end text f colon R minus left curly bracket 5 divided by 2 right curly bracket not stretchy rightwards arrow R minus left curly bracket negative 1 right curly bracket text is defined by end text f left parenthesis x right parenthesis equals fraction numerator 2 x plus 3 over denominator 5 minus 2 x end fraction text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

$text If end text f colon R minus left curly bracket 5 divided by 2 right curly bracket not stretchy rightwards arrow R minus left curly bracket negative 1 right curly bracket text is defined by end text f left parenthesis x right parenthesis equals fraction numerator 2 x plus 3 over denominator 5 minus 2 x end fraction text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

MathematicsFunctions

$text Let end text f colon N not stretchy rightwards arrow Y text be a function defined as end text f left parenthesis x right parenthesis equals 4 x plus 3 text where end text Y equals left curly bracket y element of N colon y equals 4 x plus 3 text for some end text x element of N right curly bracket.$
Inverse of f is ?

$text Let end text f colon N not stretchy rightwards arrow Y text be a function defined as end text f left parenthesis x right parenthesis equals 4 x plus 3 text where end text Y equals left curly bracket y element of N colon y equals 4 x plus 3 text for some end text x element of N right curly bracket.$
Inverse of f is ?

MathematicsFunctions

parallel

$f colon left square bracket negative 3 comma 3 right square bracket not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x cubed plus sin x plus open square brackets fraction numerator x squared plus 2 over denominator a end fraction close square brackets space text be an odd function when end text left square bracket times right square bracket text end text$
denotes greatest integer function then a is

$f colon left square bracket negative 3 comma 3 right square bracket not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x cubed plus sin x plus open square brackets fraction numerator x squared plus 2 over denominator a end fraction close square brackets space text be an odd function when end text left square bracket times right square bracket text end text$
denotes greatest integer function then a is

MathematicsFunctions

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

parallel

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

parallel

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

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