Question

The function $f :X \to Y$ defined by $f(x)= Sin\, x$ is one-one but not onto if $X$ and $Y$ are respectively equal to,

• A. $[\frac {-\pi}{2} \frac{\pi}{2}]$ and $[-1,1]$
• B. $[0 ,\frac{\pi}{2}] $ and $ [-1,1]$
• C. $[0,\pi]$ and $ [0,1]$
• D. $IR$ and $ IR$

Answer 1

Answer: (B)

Since $f : X \to Y$, then $f (x ) = \sin \; x$
Now, take option (c).
Domain = $\left[ 0, \frac{\pi}{2} \right]$, Range = [ - 1, 1]
For every value of x, we get unique value ol
y. But the value of y in [-1, 0) does not haw
any pre-image.
$\therefore $ Function is one-one but not onto.