Question

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?

Answer 1

a) f(g(x)) = 1 + log₂(x)

or

f(g(x)) = 1 + f(x)

b) The function f and g are not inverse functions

Explanation:

Data provided:

f(x) = log₂(x)

and,

g(x) = 2x

a) 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