Question

Assertion (A): $f\left(x\right)=1+x^2$ is a one one function from $R^{+}\to R$
Reason (R): Every strictly monotonic function is a one to one function

• 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

$f\left(x\right)=1+x^2$
$f^{\prime }\left(x\right)=2x$
Thus $f\left(x\right)$ is increasing on $x>0$ and decreasing on $x<0$.
$\therefore 1+x^2$ is one - one function from $R^{+}\to R$
because every strictly monotonic function is a one - one function.
Hence, both assertion and reason are true and reason is the correct explanation of assertion.