Let f(x) = log2(x) and g(x) = 2x.a. What is f(g(x))?b. Based on the results of part (a), what can you conclude about the functions f and g?
Accepted Solution
A:
Answer:a) f(g(x)) = 1 + log₂(x)or f(g(x)) = 1 + f(x)b) The function f and g are not inverse functionsStep-by-step explanation:Data provided:f(x) = log₂(x)and,g(x) = 2xa) Now, f(g(x)) = log₂((2x))also,we know the property of log function that,log(AB) = log A + log(B)therefore, f(g(x)) = log₂((2x)) = log₂(2) + log₂(x)or f(g(x)) = 1 + log₂(x)or f(g(x)) = 1 + f(x)b) f(g(x)) = 1 + log₂(x)and,g(f(x)) = 2(log₂(x))since, f(g(x)) ≠ g(f(x))Therefore,The function f and g are not inverse functions