the function $f(x)=log_2(x + 2)-3$ is graphed below. plot all lattice points of the inverse. use the labeled…

the function $f(x)=log_2(x + 2)-3$ is graphed below. plot all lattice points of the inverse. use the labeled points as your guide. click on the graph to plot a point. click a point to delete it.

the function $f(x)=log_2(x + 2)-3$ is graphed below. plot all lattice points of the inverse. use the labeled points as your guide. click on the graph to plot a point. click a point to delete it.

Answer

Explanation:

Step1: Find the inverse of the function

Let $y = \log_2(x + 2)-3$. First, solve for $x$ in terms of $y$. Add 3 to both sides: $y + 3=\log_2(x + 2)$. Rewrite in exponential - form: $2^{y + 3}=x + 2$. Then $x=2^{y + 3}-2$. So the inverse function is $f^{-1}(x)=2^{x + 3}-2$.

Step2: Find lattice points

Lattice points are points with integer coordinates. When $x=-3$, $f^{-1}(-3)=2^{-3 + 3}-2=1 - 2=-1$. When $x=-2$, $f^{-1}(-2)=2^{-2 + 3}-2=2 - 2=0$. When $x=-1$, $f^{-1}(-1)=2^{-1 + 3}-2=4 - 2=2$. When $x = 0$, $f^{-1}(0)=2^{0 + 3}-2=8 - 2=6$.

Answer:

The lattice points of the inverse function are $(-3,-1),(-2,0),(-1,2),(0,6)$