4) if $f(x)=x^2 + 3x - 8$, then determine the equation of $g(x)$ if $g(x)=-f(x + 1)+3$. 2

Question

Accepted Answer

# Explanation:
## Step1: Find $ f(x + 1) $
Substitute $ x + 1 $ into $ f(x) = x^2 + 3x - 8 $.
$$
\begin{align*}
f(x + 1)&=(x + 1)^2 + 3(x + 1) - 8\
&=x^2 + 2x + 1 + 3x + 3 - 8\
&=x^2 + 5x - 4
\end{align*}
$$
## Step2: Find $ -f(x + 1) $
Multiply $ f(x + 1) $ by -1.
$$
-f(x + 1)=-(x^2 + 5x - 4)=-x^2 - 5x + 4
$$
## Step3: Find $ g(x) $
Add 3 to $ -f(x + 1) $.
$$
\begin{align*}
g(x)&=-f(x + 1)+3\
&=-x^2 - 5x + 4 + 3\
&=-x^2 - 5x + 7
\end{align*}
$$
# Answer:
$ g(x)=-x^2 - 5x + 7 $

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QUESTION IMAGE

Question

Explanation:

Step1: Find \( f(x + 1) \)

Step2: Find \( -f(x + 1) \)

Step3: Find \( g(x) \)

Answer: