The point $(-9, 1)$ lies on the graph of $f(x)$. Given the transformation $g(x) = 2f(-x) + 3$, we need to find the corresponding point on the graph of $g(x)$.

1. Problem Description

The point $(-9, 1)$ lies on the graph of $f(x)$. Given the transformation $g(x) = 2f(-x) + 3$, we need to find the corresponding point on the graph of $g(x)$.

2. Solution Steps

Since the point $(-9, 1)$ is on the graph of $f(x)$, we have $f(-9) = 1$.

We are given $g(x) = 2f(-x) + 3$. We want to find a value of $x$ such that $-x = -9$, because we know the value of $f(-9)$.

From $-x = -9$, we have $x = 9$.

Now we can find the corresponding $y$ value for $g(x)$ by substituting $x = 9$ into the equation for $g(x)$:

$g(9) = 2f(-9) + 3$.

Since $f(-9) = 1$, we have

$g(9) = 2(1) + 3 = 2 + 3 = 5$.

Therefore, the corresponding point on the graph of $g(x)$ is $(9, 5)$.

3. Final Answer

(9, 5)