I am lost!! Find the inverse function of f(x)=log2(4x) Thanks

Answer 1

Remember the steps of finding the inverse.

y = log₂ (4x)

step 1. interchange the x and y variables:
x = log₂ (4y)

step2. solve this new equation for y
x = log₂ (4y) -----> 2^x = 4y , by definition
y = (1/4)(2^x)
= 2^-2 (2^x)
= 2^(x-2)

f^-1 (x) = 2^(x-2)

or

change the original to exponential form:
y = log₂ (4x) ----> 2^y = 4x
inverse ----> 2^x = 4y
y = (1/4)(2^x) = 2^(x-2)