Let f(x) = 210⋅x + 1 and g(x) = 310⋅x. If (fog)(x) = x, then x is equal to.

f(x) = 210x + 1
g(x) = 310x
f(g(x)) = x
f(310x) = 210(310⋅x) + 1 = x
610x + 1 = x
610x - x = -1
609x = -1
x = -1/609
However, the options provided seem to indicate a mistake in the question or the provided solution. Let's re-examine the problem. The given options suggest that g(x) might be defined differently, perhaps as g(x) = 310x - 1 or g(x) = 310x + 1.

Let's assume g(x) = 310x - 1. Then:
f(g(x)) = f(310x - 1) = 210(310x - 1) + 1 = x
610x - 210 + 1 = x
609x = 209
x = 209/609
This is not one of the options.

Now let's try g(x) = 310x + 1:
f(g(x)) = f(310x + 1) = 210(310x + 1) + 1 = x
610x + 210 + 1 = x
609x = -211
x = -211/609
This is also not in the options.

Let's assume there's a typo and g(x) should be 310/x. Then
f(g(x)) = f(310/x) = 210(310/x) + 1 = x
63000/x + 1 = x
63000 + x = x^2
x^2 - x - 63000 = 0
Solving this quadratic equation will give solutions for x that are not among the given options. The problem or the options need correction to have a consistent solution.