For the given functions $f$ and $g$, find $(g \circ f)(x)$.
\[
f(x)=-6 x+4, g(x)=2 x+3
\]
A. $-12 x+22$
B. $-12 x+11$
C. $12 x+11$
D. $-12 x-5$
Answer
Final Answer: The composition of the functions \(g\) and \(f\) is \((g \circ f)(x) = -12x + 11\), so the correct answer is \(\boxed{-12x + 11}\).
Step 1 ：The function \((g \circ f)(x)\) represents the composition of the functions \(g\) and \(f\), which means we substitute \(f(x)\) into \(g(x)\). So, we need to substitute \(f(x)=-6x+4\) into \(g(x)=2x+3\).
Step 2 ：Substitute \(f(x)\) into \(g(x)\) to get \(g(f(x)) = 2(-6x+4) + 3\).
Step 3 ：Simplify the expression to get \(g(f(x)) = -12x + 8 + 3\).
Step 4 ：Further simplify the expression to get \(g(f(x)) = -12x + 11\).
Step 5 ：Final Answer: The composition of the functions \(g\) and \(f\) is \((g \circ f)(x) = -12x + 11\), so the correct answer is \(\boxed{-12x + 11}\).
