Posted by Kenya on Sunday, May 1, 2011 at 11:45am.
How do you find the inverse of functions? for example how would you find the inverse of y= log8 x

Algebra  MathMate, Sunday, May 1, 2011 at 12:00pm
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.

Algebra  Kenya, Sunday, May 1, 2011 at 12:23pm
Ok that's slightly confusing.
I understand the flipping of x and y but then what do you do?
so x=log8 y
?

Algebra  MathMate, Sunday, May 1, 2011 at 1:34pm
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.}

Algebra  typo  MathMate, Sunday, May 1, 2011 at 1:43pm
8^{x} = 8^{log8(y)} = y
Simplify and solve y in terms of x.

Algebra  Webber, Sunday, May 1, 2011 at 1:49pm
MMMMmmmmmmk that helps, thanks!

Algebra :)  MathMate, Sunday, May 1, 2011 at 2:54pm
You're welcome!
Answer This Question
Related Questions
 Algebra  Given the functions f(x)=x+5/3 and g(x)=1/f^1(x)+1, find the value of...
 Advanced Algebra  What is the inverse of each of the functions defined by the ...
 Log Algebra  Find the inverse of the function y=log8 x
 Math  Inverse Functions  Find the inverses of the following functions. y = 3(x...
 Algebra  If f(x)=x^51/3, find f^1(31/96). I think the first step would be to...
 inverse  find f^1 (x). (this is asking me to find the inverse) f(x) = (x2)^2...
 Algebra  what is the inverse of the linear parent function? How would you graph...
 Math steve? reiny?  1. Let f(x)=x^5 + 2x^3 + x  1 Find f^1(3) and (f^1)'(3...
 Algebra 2  Ok, so I'm trying to find the inverse of each function. We're ...
 Functions  math  The function f is such that f(x) = a^2x^2  ax + 3b for x<...
More Related Questions