Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Mathematics

Functions

Easy

Question

$text The function end text f colon left square bracket 0 comma straight infinity right parenthesis not stretchy rightwards arrow left square bracket 0 comma straight infinity right parenthesis text defined by end text f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus x end fraction text is end text$

$One-One and onto$
$One-one but not onto$
$Onto but not one-one$
$Neither one-one nor onto$

The correct answer is: $text One-one but not onto end text$

$text Let end text x subscript 1 comma x subscript 2 element of left square bracket 0 comma straight infinity right parenthesis text and end text f open parentheses x subscript 1 close parentheses equals f open parentheses x subscript 2 close parentheses not stretchy rightwards double arrow fraction numerator x subscript 1 over denominator 1 plus x subscript 1 end fraction equals fraction numerator x subscript 2 over denominator 1 plus x subscript 2 end fraction not stretchy rightwards double arrow x subscript 1 plus x subscript 1 x subscript 2 equals x subscript 2 plus x subscript 1 x subscript 2 not stretchy rightwards double arrow x subscript 1 equals x subscript 2 f text is one one. end text straight there exists text no end text x element of left square bracket 0 comma straight infinity right parenthesis text such that end text f left parenthesis x right parenthesis equals 1. space f text is not onto. end text text Hence end text straight f text is one one but not onto. end text space$

Related Questions to study

Let A = { x ε R : x is not a positive integer }. Define a function f : A → R as $f left parenthesis x right parenthesis equals fraction numerator 2 x over denominator x minus 1 end fraction text then end text f text is end text$

Let A = { x ε R : x is not a positive integer }. Define a function f : A → R as $f left parenthesis x right parenthesis equals fraction numerator 2 x over denominator x minus 1 end fraction text then end text f text is end text$

MathematicsFunctions

$text If end text f colon N not stretchy rightwards arrow bold italic R text is defined by end text f left parenthesis 1 right parenthesis equals negative 1 text and end text f left parenthesis n plus 1 right parenthesis equals 3 f left parenthesis n right parenthesis plus 2 text for end text n greater than 1 comma text then end text f text is end text$

$text If end text f colon N not stretchy rightwards arrow bold italic R text is defined by end text f left parenthesis 1 right parenthesis equals negative 1 text and end text f left parenthesis n plus 1 right parenthesis equals 3 f left parenthesis n right parenthesis plus 2 text for end text n greater than 1 comma text then end text f text is end text$

MathematicsFunctions

$text Define end text f colon Z not stretchy rightwards arrow Z text by end text f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row cell x divided by 2 end cell cell left parenthesis x text is even end text right parenthesis end cell row 0 cell left parenthesis x text is odd end text right parenthesis end cell end table close text then end text f text is end text$

$text Define end text f colon Z not stretchy rightwards arrow Z text by end text f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row cell x divided by 2 end cell cell left parenthesis x text is even end text right parenthesis end cell row 0 cell left parenthesis x text is odd end text right parenthesis end cell end table close text then end text f text is end text$

MathematicsFunctions

parallel

$text If end text f colon R not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x comma text if end text x greater than 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 5 x minus 2 comma text if end text x less or equal than 2 comma space space text then end text f text is end text space$

$text If end text f colon R not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x comma text if end text x greater than 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 5 x minus 2 comma text if end text x less or equal than 2 comma space space text then end text f text is end text space$

MathematicsFunctions

For real x, $text let end text f left parenthesis x right parenthesis equals x cubed plus 5 x plus 1 comma text end text$ then

For real x, $text let end text f left parenthesis x right parenthesis equals x cubed plus 5 x plus 1 comma text end text$ then

MathematicsFunctions

$text If end text f colon left square bracket 0 comma straight infinity right parenthesis not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x squared comma text then end text f text is end text$

$text If end text f colon left square bracket 0 comma straight infinity right parenthesis not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x squared comma text then end text f text is end text$

MathematicsFunctions

parallel

$text If end text f colon R not stretchy rightwards arrow R text is defined by end text f left parenthesis x right parenthesis equals 2 x plus vertical line x vertical line text then end text f left parenthesis 2 x right parenthesis plus f left parenthesis negative x right parenthesis minus f left parenthesis x right parenthesis equals$

$text If end text f colon R not stretchy rightwards arrow R text is defined by end text f left parenthesis x right parenthesis equals 2 x plus vertical line x vertical line text then end text f left parenthesis 2 x right parenthesis plus f left parenthesis negative x right parenthesis minus f left parenthesis x right parenthesis equals$

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals fraction numerator cos squared x plus sin to the power of 4 x over denominator sin squared x plus cos to the power of 4 x end fraction text for x∈R end text$ then f(2002) =

$text If end text f left parenthesis x right parenthesis equals fraction numerator cos squared x plus sin to the power of 4 x over denominator sin squared x plus cos to the power of 4 x end fraction text for x∈R end text$ then f(2002) =

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals 4 x minus 1 comma text if end text x greater than 4 comma space space space space space space space space space space space equals x squared minus 2 comma text if end text minus 2 less or equal than x less or equal than 3 comma space space space space space space space space space space space space equals 3 x plus 4 comma text if end text x less than negative 2 comma t h e n space fraction numerator f left parenthesis negative 3 right parenthesis plus f left parenthesis 5 right parenthesis plus f left parenthesis 0 right parenthesis plus f left parenthesis negative 1 right parenthesis over denominator f left parenthesis negative 2 right parenthesis plus f left parenthesis 1 right parenthesis plus f left parenthesis negative 5 right parenthesis plus f left parenthesis 3 right parenthesis end fraction equals$

$text If end text f left parenthesis x right parenthesis equals 4 x minus 1 comma text if end text x greater than 4 comma space space space space space space space space space space space equals x squared minus 2 comma text if end text minus 2 less or equal than x less or equal than 3 comma space space space space space space space space space space space space equals 3 x plus 4 comma text if end text x less than negative 2 comma t h e n space fraction numerator f left parenthesis negative 3 right parenthesis plus f left parenthesis 5 right parenthesis plus f left parenthesis 0 right parenthesis plus f left parenthesis negative 1 right parenthesis over denominator f left parenthesis negative 2 right parenthesis plus f left parenthesis 1 right parenthesis plus f left parenthesis negative 5 right parenthesis plus f left parenthesis 3 right parenthesis end fraction equals$

MathematicsFunctions

parallel

The number of functions from {1,2,3,.....20} onto {1,2,3,......,20} such that f(k) is a multiple of 3 whenever K is a multiple of 4 is

The number of functions from {1,2,3,.....20} onto {1,2,3,......,20} such that f(k) is a multiple of 3 whenever K is a multiple of 4 is

MathematicsFunctions

The number of linear functions which map from $text end text left square bracket negative 1 comma 1 right square bracket text onto end text left square bracket 0 comma 2 right square bracket text is end text$

The number of linear functions which map from $text end text left square bracket negative 1 comma 1 right square bracket text onto end text left square bracket 0 comma 2 right square bracket text is end text$

MathematicsFunctions

Let A and B are two sets such that $A intersection B equals left curly bracket 1 comma 2 right curly bracket comma A union B equals left curly bracket 1 comma 2 comma 3 comma 4 comma 5 right curly bracket text . If end text n subscript 1 comma n subscript 2 text are end text$ maximum and minimum number of functions from A to B respectively, then n₁ - n₂ =

Let A and B are two sets such that $A intersection B equals left curly bracket 1 comma 2 right curly bracket comma A union B equals left curly bracket 1 comma 2 comma 3 comma 4 comma 5 right curly bracket text . If end text n subscript 1 comma n subscript 2 text are end text$ maximum and minimum number of functions from A to B respectively, then n₁ - n₂ =

MathematicsFunctions

parallel

If a set A contains 10 elements and a set B contains 20 elements then the number of functions from A into B is

If a set A contains 10 elements and a set B contains 20 elements then the number of functions from A into B is

MathematicsFunctions

Consider the function $f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 2 x plus 3 comma x less or equal than 1 end cell row cell negative x squared plus 6 comma x greater than 1 end cell end table close$ . then draw the graph of the function $y equals vertical line f left parenthesis x right parenthesis vertical line$

Consider the function $f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 2 x plus 3 comma x less or equal than 1 end cell row cell negative x squared plus 6 comma x greater than 1 end cell end table close$ . then draw the graph of the function $y equals vertical line f left parenthesis x right parenthesis vertical line$

MathematicsFunctions

Tell the time the clock shows.

Tell the time the clock shows.

MathematicsGrade-1

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.