Bijective Function

Q. A function f from the set of natural numbers to integers defined by f(n)=$\{\begin{array}{cc}\frac{n-1}{2},& \text{where n is odd}\\ -\frac{n}{2},& \text{where n is even}\end{array}$ is

1. One-one but not onto
2. One-one and onto both
3. Onto but not one-one
4. Neither one-one nor onto

Q. Let f: R $\to$ R be function defined by f(x) = $x^3$ + 4. Then fis

1. Injective
2. surjective
3. None of these
4. bijective

Q. Let $f:[0,\sqrt{3}]\to [0,\frac{\pi }{3}+lo{g}_{e}2]$ defined by $f\left(x\right)=lo{g}_e\sqrt{x^2+1}+ta{n}^{-1}x$ then f(x)is

1. One – one and onto
2. One – one but not onto
3. Onto but not one – one
4. Neither one – one nor onto

Q.

Describe Relations And Functions

Q. If $N\to N$ is defined by $f\left(n\right)=n-(-1{)}^n$ , then

1. f is both one-one and onto
2. f is one-one but not onto
3. f is onto but not one-one
4. f is neither one-one nor onto

Q. Given $A=x,y,z,B=u,v,w$, the function $f:A\to B$ defined by $f\left(x\right)=u,f\left(y\right)=v,f\left(z\right)=w$ is

1. Injective
2. Surjective
3. Bijective
4. All of the above

Q. If a function is onto, then it can't be _____ function.

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

Q. For mapping from A to B to be a many - one function, 4 of set A can be mapped with __ of set B.

1. 1
2. 2
3. 6
4. 7

Q. A is the set of all the numbers on which a function is defined. It may be real as well.

1. range
2. co-domain
3. domain