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Mathematics

Functions

Easy

Question

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

$2 x$
$2 | x |$
$- 2 x$
$- 2 | x |$

The correct answer is: $2 vertical line x vertical line$

$text If end text x greater or equal than 0 text then end text f left parenthesis x right parenthesis equals 2 x plus vertical line x vertical line equals 3 x. text If end text x less than 0 text then end text f left parenthesis x right parenthesis equals 2 x plus vertical line x vertical line equals x text Suppose end text x greater or equal than 0. text Then end text f left parenthesis 2 x right parenthesis plus f left parenthesis negative x right parenthesis minus f left parenthesis x right parenthesis equals 3 left parenthesis 2 x right parenthesis minus x minus 3 x equals 2 x equals 2 vertical line x vertical line table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row cell text Suppose end text x less than 0. text Then end text f left parenthesis 2 x right parenthesis plus f left parenthesis negative x right parenthesis minus f left parenthesis x right parenthesis equals 2 x plus 3 left parenthesis negative x right parenthesis minus x equals negative 2 x equals 2 vertical line x vertical line end cell row blank end table$

Related Questions to study

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

Simon likes to read 1 hour after 4o’clock. which clock shows the time Simon might read?

Simon likes to read 1 hour after 4o’clock. which clock shows the time Simon might read?

MathematicsGrade-1

The one hour before of 8 o’clock is _____.

The one hour before of 8 o’clock is _____.

MathematicsGrade-1

Two hours after 10 o’clock is _____.

Two hours after 10 o’clock is _____.

MathematicsGrade-1

parallel

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