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Mathematics

Functions

Easy

Question

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

A function
One one
Onto
One one onto

The correct answer is: Onto

$text If end text 2 less than f left parenthesis x right parenthesis less than 8 text then end text x text has two values: end text therefore f colon R not stretchy rightwards arrow R text is not one one. end text text Range of end text f text is end text R not stretchy rightwards double arrow f colon R not stretchy rightwards arrow R text is onto. end text$

Related Questions to study

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

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

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

MathematicsFunctions

parallel

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

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

parallel

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

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

parallel

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

Find the time the clock shows.

Find the time the clock shows.

MathematicsGrade-1

parallel

Choose the clock which shows the time 9 o’clock.

Choose the clock which shows the time 9 o’clock.

MathematicsGrade-1

Which clock shows the time as 11 o’clock?

Which clock shows the time as 11 o’clock?

MathematicsGrade-1

Danny starts playing a cricket match one hour after 5 o’clock. What time did he start playing the match?

Danny starts playing a cricket match one hour after 5 o’clock. What time did he start playing the match?

MathematicsGrade-1

parallel

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