Advertisements
Advertisements
प्रश्न
Which one of the following graphs is a function of x?
 |
 |
| Graph A | Graph B |
उत्तर
Graph A represents the function of x.
In graph B, we see that for a value of x, there are 2 values of y.
APPEARS IN
संबंधित प्रश्न
Check the injectivity and surjectivity of the following function:
f: Z → Z given by f(x) = x3
Show that the modulus function f: R → R given by f(x) = |x| is neither one-one nor onto, where |x| is x, if x is positive or 0 and |x| is − x if x is negative.
Show that the Signum Function f: R → R, given by `f(x) = {(1, if x > 0), (0, if x = 0), (-1, if x < 0):}` is neither one-one nor onto
Let f: R → R be defined as f(x) = 3x. Choose the correct answer.
Give examples of two functions f: N → Z and g: Z → Z such that g o f is injective but gis not injective.
(Hint: Consider f(x) = x and g(x) =|x|)
Let S = {a, b, c} and T = {1, 2, 3}. Find F−1 of the following functions F from S to T, if it exists.
F = {(a, 2), (b, 1), (c, 1)}
Give an example of a function which is neither one-one nor onto ?
Classify the following function as injection, surjection or bijection : f : Z → Z given by f(x) = x2
Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : `f (x) = x/2`
Set of ordered pair of a function? If so, examine whether the mapping is injective or surjective :{(x, y) : x is a person, y is the mother of x}
Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.
Let f : N → N be defined by
`f(n) = { (n+ 1, if n is odd),( n-1 , if n is even):}`
Show that f is a bijection.
[CBSE 2012, NCERT]
Find gof and fog when f : R → R and g : R → R is defined by f(x) = x2 + 8 and g(x) = 3x3 + 1 .
Find gof and fog when f : R → R and g : R → R is defined by f(x) = 8x3 and g(x) = x1/3.
Find fog and gof if : f (x) = x+1, g (x) = sin x .
Consider f : R+ → [−5, ∞) given by f(x) = 9x2 + 6x − 5. Show that f is invertible with `f^-1 (x) = (sqrt (x +6)-1)/3 .`
Let \[f : \left[ - \frac{\pi}{2}, \frac{\pi}{2} \right] \to\] A be defined by f(x) = sin x. If f is a bijection, write set A.
The inverse of the function
\[f : R \to \left\{ x \in R : x < 1 \right\}\] given by
\[f\left( x \right) = \frac{e^x - e^{- x}}{e^x + e^{- x}}\] is
Let \[f\left( x \right) = \frac{1}{1 - x} . \text{Then}, \left\{ f o \left( fof \right) \right\} \left( x \right)\]
Mark the correct alternative in the following question:
Let f : R→ R be defined as, f(x) = \[\begin{cases}2x, if x > 3 \\ x^2 , if 1 < x \leq 3 \\ 3x, if x \leq 1\end{cases}\]
Then, find f( \[-\]1) + f(2) + f(4)
A function f: R→ R defined by f(x) = `(3x) /5 + 2`, x ∈ R. Show that f is one-one and onto. Hence find f−1.
If f(x) = `(x+3)/(4x−5) , "g"(x) = (3+5x)/(4x−1)` then verify that `("fog") (x)` = x.
Let f: R → R be defined by f(x) = 3x – 4. Then f–1(x) is given by ______.
For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is injective. Then both f and g are injective functions.
Let f: R → R be defined by f(x) = `1/x` ∀ x ∈ R. Then f is ______.
The function f : A → B defined by f(x) = 4x + 7, x ∈ R is ____________.
Let f : R → R, g : R → R be two functions such that f(x) = 2x – 3, g(x) = x3 + 5. The function (fog)-1 (x) is equal to ____________.
A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever
Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:
R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}
- Mr. ’X’ and his wife ‘W’ both exercised their voting right in the general election-2019, Which of the following is true?
Function f: R → R, defined by f(x) = `x/(x^2 + 1)` ∀ x ∈ R is not
