Question

The image of the interval [-1, 3] under the mapping $f : R\rightarrow R$ given by $f \left(x\right)=4x^{3}-12x$ is

• A. [8, 72]
• B. [0, 72]
• C. [-8, 72]
• D. [0, 8]
• E. [-8, 8]

Answer 1

Answer: (C)

Given curve is
$f(x)=4 x^{3}-12 x, f: R \rightarrow R$
and interval $[-1,3]$.
$\therefore \, f(-1)=4(-1)^{3}-12(-1)=-4+12=8$
$f(0)=4(0)^{3}-12(0)=0 $
$f(1)=4(1)^{3}-12(1)=4-12=-8 $
$f(2)=4(2)^{3}-12(2)=32-24=8$
and $f(3)=4(3)^{3}-12(3)=108-36=72$
So, the required image is $[-8,72]$.