Given function : [tex]f(x) = 4x^3 -12x^2 + 40x + 12[/tex].
We need to find the values of f(-2).
In order to find the value of f(-2), we need to plug x=-2 in the given fucntion [tex]f(x) = 4x^3 -12x^2 + 40x + 12[/tex].
Replacing x by -2, we get
[tex]f(-2) = 4(-2)^3 -12(-2)^2 + 40(-2) + 12[/tex]
We get (-2)^2 = -2 *-2*-2=-8 and (-2)^2 = -2 * -2 = 4.
[tex]f(-2) = 4(-8) -12(4) +40(-2) +12[/tex] .
[tex]f(-2) = -32 -48 -80+12.[/tex]
f(-2) = -160 +12.
f(-2) = -148.
Therefore, correct option would be option D. That is f(-2)=-148.
