Question

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

• A. One –One into
• B. One –one onto
• C. Many one into
• D. Many one onto

Answer 1

The correct option is B

One –one onto

Here, the important thing we have to notice is that the domain is not R.

It is $[\frac{-\pi }{2},\frac{\pi }{2}]$. Now if we draw a graph of sin x for the domain $\left[\frac{-\pi }{2}\frac{\pi }{2}\right]$.). We’ll see that on the graph if we draw lines parallel to x-axis we’ll not find even a single line which would cut the graph more than once. So the function is one - one.Now we have to check whether the function is onto or not. The co- domain given is $[-1,1]$. By drawing the graph itself we can see that the function is ranging from $[-1,1]$. So the function is onto as well. Hence, f(x)= sin(x) defined on f: $\left[\frac{-\pi }{2}\frac{\pi }{2}\right]\to [-1,1]$ is one- one onto.