If f(x) = 3x/(x - 2), then f(g(x)) = [3(5x - 1)]/[(5x - 1) - 2] = (15x - 3)/(5x - 3)
f(g(3)) = (15 * 3 - 3)/(5 * 3 - 3) = (45 - 3)/(15 - 3) = 42/12 = 7/2 = 3 1/2
g(f(x)) = 5[3x/(x - 2)] - 1 = [15x/(x - 2)] - 1
g(f(4)) = [(15 * 4)/(4 - 2)] - 1 = (60/2) - 1= 30 - 1 = 29
Explanation: We just found the composite functions f(g(x)) and g(f(x)), respectively, and evaluated them at the given values of x. To find f(g(x)), we replace every instance of x in the function f with the function g(x). Likewise, to find g(f(x)), we replace each occurrence of x in g with the function f(x). To evaluate at the given values of x, simply substitute x = 3 and x = 4 into the respective composite functions.
