Question

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

• A. one-one and onto
• B. many-one and onto
• C. one-one and into
• D. many-one and into

Answer 1

The correct option is A one-one and 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 in 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.