To obtain a function g(x) that is a vertical shrink of f(x) by a factor of 1/2, we need to multiply f(x) by 1/2. This will compress the graph of f(x) vertically, making it half as tall as the original graph.
Thus, the function g(x) is:
g(x) = (1/2)f(x)
Substituting the expression for f(x), we get:
g(x) = (1/2)[3|x-7| + 11]
Now, we simplify this expression by distributing the 1/2 coefficient:
g(x) = (3/2)|x-7| + 11/2
So the function g(x) is g(x) = (3/2)|x-7| + 11/2.
The graph of g(x) will have the same shape as the graph of f(x), but it will be compressed vertically by a factor of 1/2, making it half as tall as the graph of f(x).