Question 209169
Hi Nick!!


Given {{{y= 2 ln(4x)}}}, you must solve for x by "undoing" all the operations that were done to it.  You must undo mult by 2, undo the "ln" function, and undo multiplication by 4.  That brings you down to x.


Start by dividing both sides by 2:
{{{y/2= ln(4x)}}}


In order to "undo" the "ln", you must raise both sides as a power of e:

{{{e^(y/2) = e^(ln(4x)) }}}

{{{e^(y/2) = 4x }}}


Last, divide both sides by 4:


{{{(e^(y/2))/4 = x}}}

In the above statements, y represents f(x).


NOW, if you interchange the x and the y, the NEW y represents the inverse function {{{f^-1(x)}}}.

{{{y=(e^(y/2))/4 = f^-1(x)}}}


R^2


Dr. Robert J. Rapalje, Retired
Seminole Community College
Florida