Onto Function

Q.

If A and B are disjoint sets, then how can you find n(A union.B ).

Q. If $f:A\to B$ is a function such that $B\subseteq f\left(A\right)$, then the function f is

1. Into
2. Onto
3. Bijective
4. Many-one

Q. Which of the following functions are onto functions?

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

Q. Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}.
A function f : A $\to$ B given by
f = {(1, 4), (2, 8), (3, 9), (4, 10)}. Identify the type of function.

1. Many-one and Onto function
2. Identity function
3. One-to-one function
4. One-to-one and Onto function

Q. Determine the range of the function f(x) defined as:
$f\left(x\right)=\frac{x^2+x+2}{x^2+x+1},xϵR$

1. $(1,\infty )$
2. $(1,\frac{11}{7})$
   
   
3. $(1,\frac{7}{3}]$
   
   
4. $(1,\frac{7}{5}]$
   

Q. An onto function is also called as____

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

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

Q.

Consider A = {1, 2, 3, 4} and B = {2, 3, 5, 9}. Is the relation f = {(1, 2), (2, 3), (3, 3), (3, 5)} a function from A to B?

Q.

If f ={(1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (6, 2)}, find the pre-images of 2. Which type of a function is f?

Q. Number of proper subsets of a set A given by $A=\{x:x^2-7x+12⩽0$ and $x\in Z\}$ is

$A=\{x:x^2-7x+12⩽0$ तथा $x\in Z\}$ द्वारा दिये गये समुच्चय A के उचित उपसमुच्चयों की संख्या है

1. 3
2. 8
3. 4
4. Infinite
   
   अनन्त

Q. find the range of f(x)=2 sin^8 x - 3 sin^4 x + 2

Q. If $x$ is real then the function $f\left(x\right)=\left(\frac{x^2-2x+4}{x^2+2x+4}\right)$ lies in the interval

1. $[1/3,3]$
2. $(-1/3,3)$
3. $(3,3)$
4. $(1/3,3)$

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. \N
2. 1
3. 2
4. 6

Q. Which of the given Relations can be called a function f : B$\to$A.

1. {(2, 7), (6, 5), (2, 8), (3, 13), (4, 12)}
2. {(2, 7), (6, 5), (1, 8), (3, 13), (4, 12)}
3. {(2, 7), (6, 5), (5, 13), (3, 13), (4, 12)}
4. {(1, 7), (2, 8), (3, 4)(5, 13), (3, 13), (4, 12)}