Final answer:
To find g(f(g(2))), understand that g is a constant function. Since f(g(f(2))) = 15 and f(x) = 2x + 7, g(f(g(2))) equals the constant value of g, which is 4.
Step-by-step explanation:
The question asks to find the value of g(f(g(2))) given that g is a constant function, f(x) is defined as f(x) = 2x + 7, and that f(g(f(2))) = 15. To approach this, we first need to work out f(2), which gives us f(2) = 2(2) + 7 = 11. Since g is a constant function, it means g(anything) will always yield the same value, hence g(11) and g(2) are equal. To find this constant value, we use the provided equation f(g(f(2))) = 15. Substituting the known value of f(2), we have f(g(11)) = 15, and from the definition of f(x), we get 2g(11) + 7 = 15, leading to g(11) = 4 after solving. This implies that g(x) at any x equals 4. Thus, g(f(g(2))) is just g(something), which we've established is 4, leading to the correct answer being g(f(g(2))) = 4.