Bijective Function

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.

$f:R\to R,f\left(x\right)=x|x|is$

1. one-one but not onto

2. onto but not one-one

3. Both one-one and onto

4. neither one-one nor onto

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

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

Q.

$Letf:[0,\sqrt{3}]\to [0,\frac{\pi }{3}+lo{g}_{e}2]definedf\left(x\right)=lo{g}_e\sqrt{x^2+1}+ta{n}^{-1}xthenf\left(x\right)is$

1. one – one and onto

2. one – one but not onto

3. onto but not one – one

4. neither one – one nor onto

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

Q.

f(x) = sin(x) defined on f: $[\frac{-\pi }{2},\frac{\pi }{2}]$ $\to$ $[-1,1]$ is -

1. One –One into

2. One –one onto

3. Many one into

4. Many one onto

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. Onto but not one-one
3. One-one and onto both
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. bijective
4. None of these

Q.

f(x) = $a^x$ (where a >1) defined on f: R $\to (0,\infty )$ is -

1. One –One into function

2. One –one onto function

3. Many one into function

4. Many one onto function

Q.

Given $A=\{x,y,z,\}B=\{u,v,w\},thefunctionf:A\to Bdefinedbyf\left(x\right)=u,f\left(y\right)=v,f\left(z\right)=w$ is

1. Surjective

2. bijective

3. all of the above

4. injective