Question

use the function $f(x) = 2x^3 - 3x^2 + 7$ to complete the exercises. $f(-1) = \square$ $f(1) = \square$ $f(2) = \square$

Explanation:

Step1: Substitute $x=-1$ into $f(x)$

$f(-1)=2(-1)^3 - 3(-1)^2 + 7$

Step2: Calculate each term

$2(-1)^3 = -2$, $-3(-1)^2 = -3$, so $f(-1)=-2-3+7$

Step3: Compute final value for $f(-1)$

$f(-1)=2$

Step4: Substitute $x=1$ into $f(x)$

$f(1)=2(1)^3 - 3(1)^2 + 7$

Step5: Calculate each term

$2(1)^3 = 2$, $-3(1)^2 = -3$, so $f(1)=2-3+7$

Step6: Compute final value for $f(1)$

$f(1)=6$

Step7: Substitute $x=2$ into $f(x)$

$f(2)=2(2)^3 - 3(2)^2 + 7$

Step8: Calculate each term

$2(2)^3 = 16$, $-3(2)^2 = -12$, so $f(2)=16-12+7$

Step9: Compute final value for $f(2)$

$f(2)=11$

Answer:

$f(-1)=2$
$f(1)=6$
$f(2)=11$