Bijective Function

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. Let a relation $f$ defined on $(0,\infty )$ as $f\left(x\right)=|1-\frac{1}{x}|$. Then which among the following is true

1. $f$ is many-one function
2. $f(-1)=2$
3. Relation $f$ is not a function
4. $f$ is one-one function

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. Let $f\left(x\right)=x+2$ and $g\left(x\right)=cx+d,c\ne 0$. If $\left(fog\right)\left(x\right)=\left(gof\right)\left(x\right)$ for all $x,$ then $c$ is

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.

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

1. one – one and onto

2. one – one but not onto

3. onto but not one – one

4. neither one – one nor onto

Q. 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. The number of bijection functions that can be defined from set $A$ to set $B$ is $24,$ then $n\left(A\right)+n\left(B\right)$ is