# Onto Function

## Trending Questions

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

- 14
- 16
- 12
- 8

**Q.**Let a function f defined from R→R as f(x)={2m−x, x≤14mx+1, x>1

If function is onto on R, then range of m is

- [−1, ∞)
- [−1, 0)
- {-1}
- (0, ∞)

**Q.**Let f, g:R→R be functions defined by f(x)={[x], x<0|1−x|, x≥0 and g(x)={ex−x, x<0(x−1)2−1, x≥0

where [x] denote the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly :

- four points
- one point
- two points
- three points

**Q.**Let A={1, 3, 5, 7}, B={2, 4, 6, 8} and f:A→B. Then number of functions f such that f(i)≠i+1, ∀ i=1, 3, 5, 7 is

- 64
- 24
- 256
- 81

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

- nP2
- 2n−1
- 2n−2
- (n−1)!

**Q.**Let a function f defined from R→R as f(x)={x+p2, x≤22px+5, x>2.

If the function is surjective, then sum of all possible integral value of p in [-100, 100] is

**Q.**

Using identities, evaluate ${998}^{2}$

**Q.**If set A has 3 elements and set B has 4 elements, then number of injective functions that can be defined from A to B is

- 144
- 12
- 24
- 64

**Q.**the range of the function f(x) = sin cos (ln(x^2+1/x^2+e) is

**Q.**Let A={1, 2, 3, ...., 10} and f:A→A be defined as f(k)={k+1if k is oddkif k is even. Then the number of possible functions g:A→A such that gof=f is:

- 105
- 10C5
- 55
- 5!

**Q.**If sgn(y) denotes the signum function of y, then the range of f(x)=sgn(x2+4x+5) is

- [1, ∞)
- {−1, 0, 1}
- {1}
- {0, 1}

**Q.**Let f:R→R be a differentiable function with f(0)=0. If y=f(x) satisfies the differential equation

dydx=(2+5y)(5y−2)

then the value of lim x→−∞f(x) is

**Q.**

Using identities, evaluate ${99}^{2}$

**Q.**

Let $f$ and $g$ be differentiable functions on $R$, such that $fog$ is the identity function. If for some $a,b\in R$, $g\left(a\right)=5$ and $g\left(a\right)=b$, then $f\left(b\right)$ is equal to

$\frac{2}{5}$

$5$

$1$

$\frac{1}{5}$

**Q.**Find the number of all onto functions from the set {1, 2, 3, … , n ) to itself.

**Q.**For any real valued function satisfying f(x)-sin(x)(f(x)-1)<=0 for all real x and f(0)=1, then find the range of f(x). (A)(-infinity, 1] (B)[-1, 1] (C)[1, infinity) (D)(-1, 1)

**Q.**If f:R→(−∞, a] defined by f(x)=−x2+6x+15 is surjective, then the value of a is

**Q.**Let R1 and R2 be two relations defined as follows:

R1={(a, b)∈R2:a2+b2∈Q} and

R2={(a, b)∈R2:a2+b2∉Q}, where Q is the set of all rational numbers. Then :

- R1 is transitive but R2 is not transitive.
- R1 and R2 are both transitive.
- R2 is transitive but R1 is not transitive.
- Neither R1 nor R2 is transitive.

**Q.**Check the injectivity and surjectivity of the following functions: (i) f : N → N given by f ( x ) = x 2 (ii) f : Z → Z given by f ( x ) = x 2 (iii) f : R → R given by f ( x ) = x 2 (iv) f : N → N given by f ( x ) = x 3 (v) f : Z → Z given by f ( x ) = x 3

**Q.**Let R→R be function defined as

f(x)=asin(π[x]2)+[2−x], a ∈ R, where [t] is the greatest integer less than or equal to t. If limx→−1f(x) exists, then the value of 4∫0f(x)dx is equal to

**Q.**Let A = R − {3} and B = R − {1}. Consider the function f : A → B defined by . Is f one-one and onto? Justify your answer.

**Q.**Prove that the function f given by f(x)=x2−x+1 is neither strictly increasing nor strictly decreasing on (−1, 1).

**Q.**Which of the following functions are onto functions?

- f:R→[−1, 1] as f(x)=sin(x)
- f:R→[−1, 1] as f(x)=cos(x)
- f:R→(0, ∞) as f(x)=ex
- f:R→(−∞, ∞) as f(x)=x3

**Q.**

What type of function is the sine function in R ?

many one

one-one and onto

neither onto nor one-one

one-one

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

- x+1, x-1
- -1+x, -1-x
- x+1, 1-x
- x+1, -x-1

**Q.**Let f:R→R be a function defined by f(x)=x3+x2+3x+sinx. Then f is

- injective and surjective
- injective but not surjective
- neither injective nor surjective
- surjective but not injective

**Q.**Which among the following functions are invertible?

- f:Z→Z defined by f(x)=|x|
- f:Z→Z defined by f(x)=x+2
- f:Z→Z defined by f(x)=x3
- f:Z→Z defined by f(x)=2x

**Q.**Which among the following functions are invertible?

- f:Z→Z defined by f(x)=x+2
- f:Z→Z defined by f(x)=x3
- f:Z→Z defined by f(x)=|x|
- f:Z→Z defined by f(x)=2x

**Q.**Show that the Signum Function f : R → R , given by is neither one-one nor onto.

**Q.**

Choose the correct answer.

Let,
where 0 ≤ *θ*≤ 2π,
then

A. Det (A) = 0

B. Det (A) ∈ (2, ∞)

C. Det (A) ∈ (2, 4)

D. Det (A)∈ [2, 4]