Question

1. $f(x) = 4x^3 + 12$, $g(x) = 2x^2 - 3x^3 + 9$; $x = 2$

Explanation:

Assuming we need to find \( f(2) \) and \( g(2) \) (or maybe their sum, difference, etc., but since the exact operation isn't clear, let's compute both at \( x = 2 \)):

for \( f(2) \):

Step1: Substitute \( x = 2 \) into \( f(x) \)

\( f(2)=4(2)^{3}+12 \)

Step2: Calculate \( 2^{3}=8 \)

\( f(2)=4\times8 + 12 \)

Step3: Multiply \( 4\times8 = 32 \)

\( f(2)=32+12 \)

Step4: Add \( 32 + 12=44 \)

\( f(2) = 44 \)

for \( g(2) \):

Step1: Substitute \( x = 2 \) into \( g(x) \)

\( g(2)=2(2)^{2}-3(2)^{3}+9 \)

Step2: Calculate \( 2^{2}=4 \) and \( 2^{3}=8 \)

\( g(2)=2\times4-3\times8 + 9 \)

Step3: Multiply \( 2\times4 = 8 \) and \( 3\times8 = 24 \)

\( g(2)=8-24 + 9 \)

Step4: Subtract and add: \( 8-24=-16 \), then \( -16 + 9=-7 \)

\( g(2)=-7 \)

If we assume we need to find \( f(2)+g(2) \):

Step1: Add the results of \( f(2) \) and \( g(2) \)

\( f(2)+g(2)=44+(-7) \)

Step2: Calculate the sum

\( f(2)+g(2)=37 \)

(If the intended operation was different, adjust accordingly. The above shows calculations for \( f(2) \), \( g(2) \), and their sum as examples.)

Answer:

(for \( f(2) \)): \( 44 \)