Let f:[-1,3] arrow[-8,72] be defined as f(x)=4 x3-12 x, then f is

Question

Let f:[-1,3] arrow[-8,72] be defined as f(x)=4 x3-12 x, then f is (A) injective but not surjective (B) injective as well as surjective (C) neither injective nor surjective (D) surjective but not injective

Tardigrade Admin · Accepted Answer

f(x)=4 x3-12 x f prime(x)=12(x2-1)=12(x+1)(x-1)

Q. Let $f : [- 1, 3] \to [- 8, 72]$ be defined as $f (x) = 4 x^{3} - 12 x$ , then $f$ is

injective but not surjective

injective as well as surjective

neither injective nor surjective

surjective but not injective

$f (x) = 4 x^{3} - 12 x$
$f^{'} (x) = 12 (x^{2} - 1) = 12 (x + 1) (x - 1)$

Q. Let f:[−1,3]→[−8,72] be defined as f(x)=4x3−12x, then f is