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.

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

1. Many one onto

2. One –One into

3. One –one onto

4. Many one into

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. injective

4. all of the above

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. Neither one – one nor onto
4. Onto but not 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. 2
2. 7
3. 1
4. 6