Maths-

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Question

Let $A equals R minus left curly bracket 3 right curly bracket comma B equals R minus left curly bracket 1 right curly bracket text Let end text f colon A not stretchy rightwards arrow B$ be defined by $f left parenthesis x right parenthesis equals fraction numerator x minus 2 over denominator x minus 3 end fraction$ .Then,

$f$ is bijective
$f$ is one-one but not onto
$f$ is onto but not one-one

The correct answer is: $f$ is bijective

Let X and Y be two arbitary elements in A.
Then, $f left parenthesis x right parenthesis equals f left parenthesis y right parenthesis$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow fraction numerator x minus 2 over denominator x minus 3 end fraction equals fraction numerator y minus 2 over denominator y minus 3 end fraction end cell row cell not stretchy rightwards double arrow x y minus 3 x minus 2 y plus 6 equals x y minus 3 y minus 2 x plus 6 end cell row cell not stretchy rightwards double arrow x equals y comma straight for all x comma y element of A end cell end table$
So, $f$ is an injective mapping.
Again, let Y be an orbitary element in B , then
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell f left parenthesis x right parenthesis equals y end cell row cell not stretchy rightwards double arrow fraction numerator x minus 2 over denominator x minus 3 end fraction equals y end cell row cell not stretchy rightwards double arrow x equals fraction numerator 3 y minus 2 over denominator y minus 1 end fraction end cell end table$
Clearly, $straight for all y element of B comma x equals fraction numerator 3 y minus 2 over denominator y minus 1 end fraction element of A$ , thus for all $y element of B$ there exists $x element of A$ such that
$f left parenthesis x right parenthesis equals f open parentheses fraction numerator 3 y minus 1 over denominator y minus 1 end fraction close parentheses equals fraction numerator fraction numerator 3 y minus 2 over denominator y minus 1 end fraction minus 2 over denominator fraction numerator 3 y minus 2 over denominator y minus 1 end fraction minus 3 end fraction equals y$
Thus, every element in the codomain B has its preimage in A , so $f$ is a surjection. Hence, $f colon A not stretchy rightwards arrow B$ is bijective.

The mapping $f colon N not stretchy rightwards arrow N$ given $f left parenthesis n right parenthesis equals 1 plus n squared comma n element of N$ where N is the set of natural number, is

maths-General

General

maths-

The function $f colon R not stretchy rightwards arrow R$ defined by $f left parenthesis x right parenthesis equals left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis$ is

maths-General

General

maths-

Let A be a set containing 10 distinct elements, then the total number of distinct function from A to A is

maths-General

General

maths-

$A equals left curly bracket 1 comma 2 comma 3 comma 4 right curly bracket comma B left curly bracket 1 comma 2 comma 3 comma 4 comma 5 comma 6 right curly bracket$ are two sets, and function $f colon A not stretchy rightwards arrow B$ is defined by $f left parenthesis x right parenthesis equals x plus 2 straight for all x element of A$ , then the function $f$ is

maths-General

General

maths-

Let $n left parenthesis A right parenthesis equals 4 text and end text n left parenthesis B right parenthesis equals 6$ and The number of one to one functions from A to B is

maths-General

General

maths-

If denotes the set of all real numbers, then the function $f colon R not stretchy rightwards arrow R$ defined by $f left parenthesis x right parenthesis equals vertical line x vertical line$ is

maths-General

General

maths-

If $f colon R not stretchy rightwards arrow C$ is defined by $f left parenthesis x right parenthesis equals e to the power of 2 i x end exponent$ for $x element of R$ , then $f$ is (where C denotes the set of all complex numbers)

maths-General

General

maths-

Let $A equals left square bracket negative 1 comma 1 right square bracket text and end text f colon A not stretchy rightwards arrow A$ be defined as $f left parenthesis x right parenthesis equals x vertical line x vertical line text for all end text x element of A text , then end text f left parenthesis x right parenthesis$ is

maths-General

General

maths-

Let $f colon N not stretchy rightwards arrow N$ defined by $f left parenthesis x right parenthesis equals x squared plus x plus 1 comma x element of N$ , then $f$ is

maths-General

General

maths-

Q function $f$ from the set of natural numbers to integers defined by $f left parenthesis n right parenthesis equals open curly brackets table attributes columnalign left columnspacing 1em end attributes row cell fraction numerator n minus 1 over denominator 2 end fraction comma text where end text n text is odd end text end cell row cell negative n over 2 comma text when end text n text is even end text end cell end table close$ is

maths-General

General

maths-

Let be the set of all real numbers Then, the relation $R equals left curly bracket left parenthesis a comma b right parenthesis colon 1 plus a b greater than 0 right curly bracket$ on S is

maths-General

General

maths-

The relation defined on the set of natural numbers as {(a,b) a differs from b by 3} is given by

maths-General

General

maths-

Let {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set $A equals left curly bracket 3 comma 6 comma 9 comma 12 right curly bracket$ The relation is

maths-General

General

Let $R equals left curly bracket left parenthesis 1 comma 3 right parenthesis comma left parenthesis 4 comma 2 right parenthesis comma left parenthesis 2 comma 4 right parenthesis comma left parenthesis 2 comma 3 right parenthesis comma left parenthesis 3 comma 1 right parenthesis right curly bracket$ be a relation on the set $A equals left curly bracket 1 comma 2 comma 3 comma 4 right curly bracket$ The relation R is

In this question, we have to find the which type of relation it is. Try to prove the all type of relation and find the which one is satisfies it.

Let $R equals left curly bracket left parenthesis 1 comma 3 right parenthesis comma left parenthesis 4 comma 2 right parenthesis comma left parenthesis 2 comma 4 right parenthesis comma left parenthesis 2 comma 3 right parenthesis comma left parenthesis 3 comma 1 right parenthesis right curly bracket$ be a relation on the set $A equals left curly bracket 1 comma 2 comma 3 comma 4 right curly bracket$ The relation R is

GeneralGeneral

In this question, we have to find the which type of relation it is. Try to prove the all type of relation and find the which one is satisfies it.

General

maths-

Five coins whose faces are marked 3,4 are thrown. The chance of obtaining a total of 18 is

maths-General

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Can’t find what you’re looking for?

Let be defined by .Then,

is bijective is one-one but not onto is onto but not one-one

The correct answer is: is bijective

Let X and Y be two arbitary elements in A.Then, So, is an injective mapping.Again, let Y be an orbitary element in B , thenClearly, , thus for all there exists such thatThus, every element in the codomain B has its preimage in A , so is a surjection. Hence, is bijective.

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The function defined by is

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Let A be a set containing 10 distinct elements, then the total number of distinct function from A to A is

Let A be a set containing 10 distinct elements, then the total number of distinct function from A to A is

are two sets, and function is defined by , then the function is

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Five coins whose faces are marked 3,4 are thrown. The chance of obtaining a total of 18 is

Five coins whose faces are marked 3,4 are thrown. The chance of obtaining a total of 18 is

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$f$ is bijective
$f$ is one-one but not onto
$f$ is onto but not one-one

The correct answer is: $f$ is bijective

The mapping $f colon N not stretchy rightwards arrow N$ given $f left parenthesis n right parenthesis equals 1 plus n squared comma n element of N$ where N is the set of natural number, is

The mapping $f colon N not stretchy rightwards arrow N$ given $f left parenthesis n right parenthesis equals 1 plus n squared comma n element of N$ where N is the set of natural number, is

The function $f colon R not stretchy rightwards arrow R$ defined by $f left parenthesis x right parenthesis equals left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis$ is

The function $f colon R not stretchy rightwards arrow R$ defined by $f left parenthesis x right parenthesis equals left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis$ is

Let $n left parenthesis A right parenthesis equals 4 text and end text n left parenthesis B right parenthesis equals 6$ and The number of one to one functions from A to B is

Let $n left parenthesis A right parenthesis equals 4 text and end text n left parenthesis B right parenthesis equals 6$ and The number of one to one functions from A to B is

If denotes the set of all real numbers, then the function $f colon R not stretchy rightwards arrow R$ defined by $f left parenthesis x right parenthesis equals vertical line x vertical line$ is

If denotes the set of all real numbers, then the function $f colon R not stretchy rightwards arrow R$ defined by $f left parenthesis x right parenthesis equals vertical line x vertical line$ is

If $f colon R not stretchy rightwards arrow C$ is defined by $f left parenthesis x right parenthesis equals e to the power of 2 i x end exponent$ for $x element of R$ , then $f$ is (where C denotes the set of all complex numbers)

If $f colon R not stretchy rightwards arrow C$ is defined by $f left parenthesis x right parenthesis equals e to the power of 2 i x end exponent$ for $x element of R$ , then $f$ is (where C denotes the set of all complex numbers)

Let $f colon N not stretchy rightwards arrow N$ defined by $f left parenthesis x right parenthesis equals x squared plus x plus 1 comma x element of N$ , then $f$ is

Let $f colon N not stretchy rightwards arrow N$ defined by $f left parenthesis x right parenthesis equals x squared plus x plus 1 comma x element of N$ , then $f$ is

Let be the set of all real numbers Then, the relation $R equals left curly bracket left parenthesis a comma b right parenthesis colon 1 plus a b greater than 0 right curly bracket$ on S is

Let be the set of all real numbers Then, the relation $R equals left curly bracket left parenthesis a comma b right parenthesis colon 1 plus a b greater than 0 right curly bracket$ on S is

Let {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set $A equals left curly bracket 3 comma 6 comma 9 comma 12 right curly bracket$ The relation is

Let {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set $A equals left curly bracket 3 comma 6 comma 9 comma 12 right curly bracket$ The relation is