Answer:
Step-by-step solution to solve g[g(x)]=g(x) for x:
1. Substitute g(x) into the equation g[g(x)]=g(x): 5(5x-8) - 8 = 5x - 8.
2. Simplify the equation: 25x - 40 = 5x - 8.
3. Subtract 5x from both sides of the equation: 25x - 5x - 40 = - 8.
4. Simplify the equation: 20x = -32.
5. Divide both sides of the equation by 20: x = -32/20.
6. Solve for x: x = -1.6.
7. The solution to the equation is x = -1.6.