Use the function f(x) = 2x3 - 3x2 + 7 to complete the exercises.

f(−1) =

f(1) =

f(2) =

1 answer

To find the values of the function \( f(x) = 2x^3 - 3x^2 + 7 \) at different points, we can substitute \( x \) with the given values and evaluate the expression.

1. For \( f(-1) \):

\[ f(-1) = 2(-1)^3 - 3(-1)^2 + 7 \]
\[ f(-1) = 2(-1) - 3(1) + 7 \]
\[ f(-1) = -2 - 3 + 7 \]
\[ f(-1) = 2 \]

2. For \( f(1) \):

\[ f(1) = 2(1)^3 - 3(1)^2 + 7 \]
\[ f(1) = 2(1) - 3(1) + 7 \]
\[ f(1) = 2 - 3 + 7 \]
\[ f(1) = 6 \]

3. For \( f(2) \):

\[ f(2) = 2(2)^3 - 3(2)^2 + 7 \]
\[ f(2) = 2(8) - 3(4) + 7 \]
\[ f(2) = 16 - 12 + 7 \]
\[ f(2) = 11 \]

So, the evaluated values are:

\[ f(-1) = 2 \]
\[ f(1) = 6 \]
\[ f(2) = 11 \]