Find gx the inverse of fx log24x 2Solutionfx log24x 2 To

Find g(x), the inverse of f(x) = log_2(4x) - 2.

f(x) = log₂(4x) - 2

To find g(x), the inverse of f(x), we have to put i/x in place of x.

Therefore, g(x) = f(1/x) = log₂(4*1/x) - 2

g(x) = log (4*1/x)/ log 2 - 2

g(x) = log 4/ log 2 + log (1/x)/ log 2 - 2

g(x) = log 2²/ log 2 + log x^-1 / log 2 - 2

g(x) = 2 log 2/ log 2 + (-1) log x/ log 2 - 2

g(x) = 2 - log x/ log 2 - 2

g(x) = - log x/ log 2

g(x) = - log₂ x

This is the final answer and inverse of f(x).