Algebra
posted by Kenya on .
How do you find the inverse of functions? for example how would you find the inverse of y= log8 x

Let's try this for f(x)= y = e^(6x)
Step 1:
interchange x and y to get
x=e^(6y)
Step 2:
solve for y in terms of x:
ln(x) = ln(e^(6y)) = 6y
y = ln(x)/6
So
f^{1}(x) = ln(x)/6
Step 3:
Verify that f(f^{1}(x))=x (if the inverse was correct).
f(f^{1}(x))
=f(ln(x)/6)
=e^(6*ln(x)/6)
=e^(ln(x))
=x
So the inverse is correct. 
Ok that's slightly confusing.
I understand the flipping of x and y but then what do you do?
so x=log8 y
? 
Yes, then you solve for y in terms of x.
use the law of exponents:
e^{log(x)}=x
or
8^{log8 y}=y, etc.
(assuming log8 y is log(y) to the base 8)
raise both sides to power of 8 to get
8^{x} = 8^{log8(y)<?sup> Simplify and solve y in terms of x.} 
8^{x} = 8^{log8(y)} = y
Simplify and solve y in terms of x. 
MMMMmmmmmmk that helps, thanks!

You're welcome!