Onto Function

Q. Let Z be the set ofall integers and A={(x, y);x4–y4=175, x, y∈ Z}B={(x, y);x>y, x, y∈ Z}Then, the number of elementsinA∩ Bis

Q.

If A = {1, 2, 3}, B = {a, b, c}, which of the following is a function?

1. R = {(1, b), (1, c), (3, a)}

2. R = {1, , a), (2, a), (1, c)}

3. R = {(1, b), (2, c), (3, a)}

4. R = {(1, c), (2, b), (2, c)}

Q. The mean value of integral ( sin theta d theta) where the limit is pie to 0 is

Q. Find the value of Sin^{10}x+Cos^{10}x=

Q. 1. Let be a set with exactly 5 elements and y be a set with exactly 7 elements. If A Is the number of one - one functions from x to y and B is the number of onto functions from y to X, then find the value of B-A/5!

Q. 29. What is the range of sin2A-cos2A and how?

Q. Let A = [p, q, r, s] and B = [1, 2, 3]. Which of the following relations from A to B is not a function?

(a) R₁ = [(p, 1), (q, 2), (r, 1), (s, 2)]
(b) R₂ = [(p, 1), (q, 1), (r, 1), (s, 1)]
(c) R₃ = [(p, 1), (q, 2), (p, 2), (s, 3)
(d) R₄ = [(p, 2), (q, 3), (r, 2), (s, 2)].

Q. Find domain and range of f(x)=sin{ln(square root of (4-(x square))/(1-x))

Q. Let A = {a, b, {c, d}, e}. Which of the following statements are false and why?
(i) $\left\{c,d\right\}\subset A$
(ii) $\left\{c,d\right\}\in A$
(iii) $\left\{\left\{c,d\right\}\right\}\subset A$
(iv) $a\in A$
(v) $a\subset A$
(vi) $\left\{a,b,e\right\}\subset A$
(vii) $\left\{a,b,e\right\}\in A$
(viii) $\left\{a,b,c\right\}\subset A$
(ix) $\varphi \in A$
(x) $\left\{\varphi \right\}\subset A$

Q.

What is the range of cos function?

1. [0, 1]

2. [-2, 2]

3. [-1, 0]

4. [-1, 1]

Q. If $f:R\to (-\infty ,a]$ defined by $f\left(x\right)=-x^2+6x+15$ is surjective, then the value of $a$ is

Q.

Which of the following function is an onto function-

1. f(x) = sin(x) on f : R $\to$ [-1, 1]

2. f(x) = cos(x) on f : R $\to$ [-1, 1]

3. f(x) = $e^x$ on f : R $\to$ $(0,\infty )$

4. All of the above.

Q. 21. Find the range of the following functions- (a) f(x)= 1/(|x| -x) (b) f(x) = (cos(sinx)) + 1/sin (1+x/2x)

Q.

If A and B are subsets of X such that $A\subseteq B.,then(X-B)\subseteq (X-A).$

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. 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. 22. How to find range of f(x)= sinx-3 cosx+1

Q. If $f\left(x\right)=\left[\right[x\left]\right]-[x-1]$ then which of the following options is CORRECT, (where $[.]$ represents the greatest integer function.)

1. Discontinuous at $x=0$
2. Discontinuous at $x=1$
3. Discontinuous at $x=-1$
4. Continuous at every where

Q. If $A=\{1,2,3,4\}$ and $B=\{5,7,9\}$, then the number of onto function from $A$ to $B$ is

1. $36$
2. $45$
3. $81$
4. $64$

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. The range of f(x)=sin^–1 (x-sqrt root of x)is

Q. 19. Find domain and range sin1 (1-|x|)/2

Q. There are exactly two distinct linear functions, which map [-1, 1] on to [0, 2], they are

1. x+1, x-1
2. -1+x, -1-x
3. x+1, 1-x
4. x+1, -x-1

Q.

Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.

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 a function f defined from $R\to R$ as $f\left(x\right)=\{\begin{array}{cc}2m-x,& x\le 1\\ 4mx+1,& x>1\end{array}$
If function is onto on R, then range of m is

1. $[-1,\infty )$
2. $[-1,0)$
3. {-1}
4. $(0,\infty )$

Q. Find domain and range of f(x)=sin{ln(square root of (4-(x square))/(1-x))