Question

Assertion(A): If $X=\{x:-1\le x\le 1\}$ and $f:X\to X$ defined by $f\left(x\right)=\sin \pi x;\forall x\in A$ is not invertible function

Reason (R): For a function $f$ to have inverse, it should be a bijection

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is not correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The correct option is A Both A and R are true and R is the correct explanation of A

$f(-\pi )=f\left(0\right)=f\left(\pi \right)=0$
$\therefore f$ is not a bijection
$\therefore \sin \pi x$ is not invertible.