Step 1 :The x-intercept of a function is the point where the function crosses the x-axis. At this point, the y-coordinate is 0. So, we need to solve the equation \(11 - 9^{(x+1)} = 0\) for x.
Step 2 :Solving for x, we get \(x = 0.09\).
Step 3 :\(\boxed{x=0.09}\)