Question 268086
{{{f(x) = log(4, (16x))}}}<br>
To find the inverse of a function:<ol><li>Replace the function notation with "y".</li><li>Swap the x's and y's. After this you have the equation for the inverse.</li><li>Solve the inverse equation for y, if possible.</li></ol>
Let's see how this works with your function.
1) Replace the function notation
{{{y = log(4, (16x))}}}
2) Swap the x's and y's
{{{x = log(4, (16y))}}}
3) Solve for y. We start by rewriting the equation in exponential form:
{{{4^x = 16y}}}
Next, divide both sides by 16:
{{{4^x/16 = y}}}
Since we were able to solve for y, the inverse of your function is itself also a function. This equation may be an acceptable answer. Or you may want to write this with function notation for an inverse:
{{{4^x/16 = f^(-1)(x)}}}
(Note: Algebra.com's formula software does not handle inverse notation well. It shows a multiplication symbol which does not belong.)<br>
Also, since 16 is a power of 4, we can simplify the left side:
{{{4^x/4^2 = f^(-1)(x)}}}
{{{4^(x-2) = f^(-1)(x)}}}