Advertisements
Advertisements
प्रश्न
Let A = {a, b, c, d} and f : A → A be given by f = {( a,b ),( b , d ),( c , a ) , ( d , c )} write `f^-1`. [NCERT EXEMPLAR]
Advertisements
उत्तर
We have ,
A = {a, b, c, d} and f : A
→ A be given by f = {(a, b), (b, d), (c, a), (d, c)}
Since, the elements of a function when interchanged gives inverse function.
so, f -1 = {(b, a), (d, b), (a, c), (c, d)}
APPEARS IN
संबंधित प्रश्न
Check the injectivity and surjectivity of the following function:
f : Z → Z given by f(x) = x2
In the following case, state whether the function is one-one, onto or bijective. Justify your answer.
f : R → R defined by f(x) = 1 + x2
Let f: R → R be defined as f(x) = 10x + 7. Find the function g: R → R such that g o f = f o g = 1R.
Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = sin2x + cos2x
Show that the function f : R − {3} → R − {2} given by f(x) = `(x-2)/(x-3)` is a bijection.
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 + 2x − 3 and g(x) = 3x − 4 .
State with reason whether the following functions have inverse :
f : {1, 2, 3, 4} → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)}
Show that the function f : Q → Q, defined by f(x) = 3x + 5, is invertible. Also, find f−1
A function f : R → R is defined as f(x) = x3 + 4. Is it a bijection or not? In case it is a bijection, find f−1 (3).
Let A = {x &epsis; R | −1 ≤ x ≤ 1} and let f : A → A, g : A → A be two functions defined by f(x) = x2 and g(x) = sin (π x/2). Show that g−1 exists but f−1 does not exist. Also, find g−1.
Let A and B be two sets, each with a finite number of elements. Assume that there is an injective map from A to B and that there is an injective map from B to A. Prove that there is a bijection from A to B.
Which of the following graphs represents a one-one function?
Let A = {x ∈ R : −4 ≤ x ≤ 4 and x ≠ 0} and f : A → R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\]Write the range of f.
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.
Write the domain of the real function
`f (x) = sqrt([x] - x) .`
If f : R → R be defined by f(x) = (3 − x3)1/3, then find fof (x).
If f(x) = 4 −( x - 7)3 then write f-1 (x).
The function
f : A → B defined by
f (x) = - x2 + 6x - 8 is a bijection if
Let
f : R → R be given by
\[f\left( x \right) = \left[ x^2 \right] + \left[ x + 1 \right] - 3\]
where [x] denotes the greatest integer less than or equal to x. Then, f(x) is
(d) one-one and onto
Let f be an injective map with domain {x, y, z} and range {1, 2, 3}, such that exactly one of the following statements is correct and the remaining are false.
\[f\left( x \right) = 1, f\left( y \right) \neq 1, f\left( z \right) \neq 2 .\]
The value of
\[f^{- 1} \left( 1 \right)\] is
Let
\[A = \left\{ x \in R : x \leq 1 \right\} and f : A \to A\] be defined as
\[f\left( x \right) = x \left( 2 - x \right)\] Then,
\[f^{- 1} \left( x \right)\] is
Let [x] denote the greatest integer less than or equal to x. If \[f\left( x \right) = \sin^{- 1} x, g\left( x \right) = \left[ x^2 \right]\text{ and } h\left( x \right) = 2x, \frac{1}{2} \leq x \leq \frac{1}{\sqrt{2}}\]
If \[f : R \to R\] is given by \[f\left( x \right) = x^3 + 3, \text{then} f^{- 1} \left( x \right)\] is equal to
Let f: R → R be the function defined by f(x) = 2x – 3 ∀ x ∈ R. write f–1
Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:
g(x) = |x|
Let f: `[2, oo)` → R be the function defined by f(x) = x2 – 4x + 5, then the range of f is ______.
The function f : R → R defined by f(x) = 3 – 4x is ____________.
Let f : R → R be a function defined by f(x) `= ("e"^abs"x" - "e"^-"x")/("e"^"x" + "e"^-"x")` then f(x) is
The mapping f : N → N is given by f(n) = 1 + n2, n ∈ N when N is the set of natural numbers is ____________.
Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then relation R is ____________.
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?
Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.
Answer the following questions using the above information.
- Let f: R → R be defined by f(x) = x2 is:
Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.
Answer the following questions using the above information.
- Let f: {1,2,3,....} → {1,4,9,....} be defined by f(x) = x2 is ____________.
The domain of the function `cos^-1((2sin^-1(1/(4x^2-1)))/π)` is ______.
If f: R→R is a function defined by f(x) = `[x - 1]cos((2x - 1)/2)π`, where [ ] denotes the greatest integer function, then f is ______.
For x ∈ R, x ≠ 0, let f0(x) = `1/(1 - x)` and fn+1 (x) = f0(fn(x)), n = 0, 1, 2, .... Then the value of `f_100(3) + f_1(2/3) + f_2(3/2)` is equal to ______.
Many students choosing the same favourite subject resembles which type of function?
