Onto Function

Q. Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of onto functions from A into B is

1. $\left(n-1\right)!$
2. $2^n-1$
3. $2^n-2$
4. $nP2$

Q. Let E = {1, 2, 3, 4} and F = {1, 2}. Then, the number of onto functions from E to F is

1. 14
2. 16
3. 12
4. 8

Q. Let f = {(2, 7), (3, 4), (7, 9), (-1, 6), (0, 2), (5, 3)} be a function from A = {-1, 0, 2, 3, 5, 7} to B = {2, 3, 4, 6, 7, 9}. Identify the type of function.

1. One-to-one
2. Both a and b
3. Onto
4. Many-to-one

Q. Which of the following functions are onto functions?

1. $f:R\to (-\infty ,\infty )$ as $f\left(x\right)=x^3$
2. $f:R\to [-1,1]$ as $f\left(x\right)=cos\left(x\right)$
3. $f:R\to (0,\infty )$ as $f\left(x\right)=e^x$
4. $f:R\to [-1,1]$ as $f\left(x\right)=sin\left(x\right)$

Q. For mapping from A to B to be an into function, 4 of set A can't be mapped with __ of set B.

1. 2
2. 1
3. 0
4. 6

Q. If A = {−2, −1, 0, 1, 2} and f : A $\to$ B is an onto function defined by f (x) = x${}^2$ + x + 1, then find B.

1. B = {1, 3}
2. B = {1, 3, 7}
3. B = {-1, 3, 7}
4. B = {-1, -3, -7}

Q. The function : $R\to [-\frac{1}{2},\frac{1}{2}]$ defined as $f\left(x\right)=\frac{x}{1+x^2}$ is

1. invertible
2. injective but not surjective
3. surjective but not injective
4. neither injective nor surjective

Q. An onto function is also called as____

1. Surjection
2. Bijection
3. None of the above
4. Injection