Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 36

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If a function $f : R \to R$ is defined by $f (x) = x^{3} + 4 x^{2} + c x + d$ , where $c, d \in R$ , if $f (x)$ is one-one onto, then $c$ may be

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Important Questions on Relation and Functions

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 37

Let

A = {1, 2, 3}, B = {a, b, c}, C = \{a_{1}, b_{1}, c_{1}, d_{1}, e_{1}\}

and consider the following statements

S_{1}

: The number of one-one functions from

A

to

C

is

60

S_{2}

:The number of onto functions from

C

to

A

is

150

S_{3}

: The number of onto functions from

B

to

C

is zero

S_{4}

: The number of bijective functions from

A

to

B

is

6

Which of the following combinations is true?

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 38

Which of the followings is not true?

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 39

Let

S

be the set of all triangles and

R^{+}

be the set of positive real numbers, then the function

f : S ⟶ R^{+}, f (Δ) =

Area of

△

,where

△ \in S

, then '

f

' is

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 40

If

f (x) = [x] & g (x) = x - [x]

then which of the following functions is the zero function

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 41

Given

f (x) = \frac{1}{(1 - x)}, g (x) = f {f (x)}

and

h (x) = f {f {f (x)}}

, then the value of

f (x) \cdot g (x) \cdot h (x)

is

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 42

Let

A = {1, 2, 3}

. Which of the following functions on

A

is invertible?

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 43

Let

f : R \to R

and

g : R \to R

be two functions given by

f (x) = 2 x - 3, g (x) = x^{3} + 5 .

Then

{(f o g)}^{- 1} (x) =

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 44

If

F : [1, \infty) \to [2, \infty)

is given by

f (x) = x + \frac{1}{x},

then

f^{- 1} (x)

equals