f(x) = -2x + 2
g(x) = (1/3)^x + 1
f(x) = g(x)
-2x + 2 = (1/3)^x + 1
-2x + 2 = 3^(-x) + 1
3^(-x) + 2x + 2 - 1 = 0
3^(-x) + 2x + 1 = 0
We don't know how to solve this, right? But we can analyse the graph. We see that both f(x) and g(x) find each other in two points, (0, 2) and (-1, 4)
So we can say that x = -1 and x = 0 are solutions for this equation.