Let $f: R→ R$ be defined as $f(x)= 10-x^2$, then:

f is neither one-one nor onto.

The correct answer is Option (3) → f is neither one-one nor onto.

$f: R→ R,f(x)= 10-x^2$

Check if $f(x)$ is one-one

$f(x_1)=f(x_2)⇒x_1=x_2$

$⇒10-x_1^2=10-x_2^2$

$⇒x_1=±x_2$

∴ Not one - one,

Check if $f(x)$ is onto,

$y=10-x^2$

$⇒x^2=10-y$

$10-y≥0⇒y≤10$

∴ Not onto