If f(x) = 4x – 1 and f(g(6)) = – 1/3, then g(x) could equal which of the following?

(A) 1/x

(B) x^{2}

(C) x/6

(D) – x/18

Solution:

**Choice A is correct.**

Since, f(g(6)) = – 1/3

Therefore, 4 g(6) – 1 = – 1/3 ( As f(x) = 4x – 1)

Hence 4 g(6) = 2/3

Or g(6) = 1/6

If g(x) = 1/x, then g(6) = 1/6 (which we derived above)

Therefore, g(x) = 1/x is a solution.