Find g(x), where g(x) is the reflection across the y-axis of f(x)=4|x+1|+1.

To find the reflection of the function f(x) = 4|x+1|+1 across the y-axis, we replace x with -x in the function.

Step 1: Identify the function f(x) = 4|x+1|+1.

Step 2: Replace every x in the function with -x.

So, f(-x) = 4|-x+1|+1.

Step 3: Simplify the function.

The absolute value of -x+1 is the same as the absolute value of x-1, because the absolute value of a number is always positive.

So, f(-x) = 4|x-1|+1.

Therefore, the function g(x) that is the reflection of f(x) across the y-axis is g(x) = 4|x-1|+1.