Question

If $f:[0,\pi ]\to R,f\left(x\right)=\cos x$, then $f$ is

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

Answer 1

The correct option is B one-one into

$f\left(x\right)$ is strictly decreasing in $(0,\pi )$
Therefore, $f$ is one one.
and range of $f\left(x\right)$ is $(-1,1)$
Therefore, $f$ is into.