Inverse of a Function

Q.

If R be a relation $<$ from A={1, 2, 3, 4} to B={1, 3, 5} i.e., (a, b) $\in R\iff a<b,thenRo{R}^{-1}$ is

1. {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

2. {(3, 1) (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}

3. {(3, 3), (3, 5), (5, 3), (5, 5)}

4. {(3, 3) (3, 4), (4, 5)}

Q.

Let A = {1, 2, 3}, B = {1, 3, 5}. A relation R:A $\to$ B is

defined by R = {(1, 3), (1, 5), (2, 1)}. Then $R^{-1}$ is defined by

1. {(1, 2), (3, 1), (1, 3), (1, 5)}

2. {(1, 2), (3, 1), (2, 1)}

3. {(1, 2), (5, 1), (3, 1)}

4. None of these

Q.

Let A = {1, 2, 3}, B = {1, 3, 5}. A relation R:A $\to$ B is

defined by R = {(1, 3), (1, 5), (2, 1)}. Then $R^{-1}$ is defined by

1. {(1, 2), (3, 1), (1, 3), (1, 5)}

2. {(1, 2), (3, 1), (2, 1)}

3. {(1, 2), (5, 1), (3, 1)}

4. None of these

Q.

The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then $R^{-1}$ is given by

1. {(1, 2), (2, 4), (3, 6)....}

2. 

3. None of these

4. {(2, 1), (4, 2), (6, 3).....}

Q. Let $f:(4,6)\to (6,8)$ be a function defined by $f\left(x\right)=x+\left[\frac{x}{2}\right]$ (where [.] denotes the greatest integer function),
then $f^{-1}\left(x\right)$ is equal to

1. $X-\left[\frac{x}{2}\right]$
2. $-x-2$
3. $x-2$
4. $\frac{1}{x+\left[\frac{\pi }{2}\right]}$

Q. If $f\left(x\right)=sinx+cosx,g\left(x\right)=x^2-1$ then $g\left(f\right(x\left)\right)$ in invertible in the Domain

1. 
2. 
3. 
4. 

Q.

If a function is defined such that its inverse exists then the domain of the function becomes the range of the inverse function

1. True

2. False

Q.

What is the inverse of the function { (1, 2), (2, 3), (3, 1) } from the set A ={1, 2, 3} to itself?

1. {(2, 1), (3, 3), (1, 2)}

2. { (1, 2), (2, 3), (3, 1) }

3. {(2, 3), (1, 2), (3, 1)}

4. None of these

Q.

If R be a relation $<$ from A={1, 2, 3, 4} to B={1, 3, 5} i.e., (a, b) $\in R\iff a<b,thenRo{R}^{-1}$ is

1. {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

2. {(3, 3) (3, 4), (4, 5)}

3. {(3, 1) (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}

4. {(3, 3), (3, 5), (5, 3), (5, 5)}

Q. $f:[2,\infty )\to (-\infty ,4],wheref\left(x\right)=x(4-x)then{f}^{-1}\left(x\right)is$

1. 
2. 
3. 
4.