Perform the indicated operations.
\[
\begin{array}{l}
g(a)=2 a+2 \\
h(a)=a^{3}-3 a \\
\text { Find }(2 g-3 h)(-3)
\end{array}
\]
A) -24
B) 46
C) -136
D) 12

Answer

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Answer

\boxed{46}\)

Steps

Step 1 ：Find the expressions for 2g(a) and 3h(a):

Step 2 ：\(2g(a) = 2(2a + 2) = 4a + 4\)

Step 3 ：\(3h(a) = 3(a^3 - 3a) = 3a^3 - 9a\)

Step 4 ：Subtract 3h(a) from 2g(a):

Step 5 ：\((2g - 3h)(a) = (4a + 4) - (3a^3 - 9a) = -3a^3 + 13a + 4\)

Step 6 ：Evaluate the expression at a = -3:

Step 7 ：\((-3(-3)^3 + 13(-3) + 4) = (-3(27) - 39 + 4) = (-81 - 39 + 4)\)

Step 8 ：\boxed{46}\)