Algebra
posted by Kenya .
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!
Respond to this Question
Similar Questions

inverse
find f^1 (x). (this is asking me to find the inverse) f(x) = (x2)^2, x <= 2 how do I solve this problem? 
Math  Inverse Functions
Find the inverses of the following functions. y = 3(x  1)^2, x >= 1 Work: x = 3(y  1)^2 x = 3(y  1)(y  1) x = 3(y^2  y  y + 1) x = 3y^2  6y + 3 And now what do I do!? 
Log Algebra
Find the inverse of the function y=log8 x 
Algebra 2
Ok, so I'm trying to find the inverse of each function. We're learning about Inverse Functions and Relations. The problem is f(x)=sqr.root of x/6 The sqr root is confusing me. 
Algebra
what is the inverse of the linear parent function? 
Algebra
If f(x)=x^51/3, find f^1(31/96). I think the first step would be to find the inverse of 31/96, but I am not sure how to find that :). Then I could make x^51/3= the inverse of 31/96. 
Algebra
Given the functions f(x)=x+5/3 and g(x)=1/f^1(x)+1, find the value of g(3). The first step would first be to find the inverse of x+1, the denominator of the fraction. I think the inverse would be 1x. And now we have 1/1x so we can … 
Advanced Algebra
What is the inverse of each of the functions defined by the following equations, if the inverse exists. If the inverse does not exist for the largest possible domain, limit the domain so that the inverse will exist. In each case, give … 
Math steve? reiny?
1. Let f(x)=x^5 + 2x^3 + x  1 Find f^1(3) and (f^1)'(3)? 
Algebra Help ASAP PLEASE!
((I forgot how to do find inverse functions and this is important)) Find the inverse function of g(x) = 2x + 4. A) g^(1)(x) = 4x + 2 B) g^(1)(x) = 2x + 1/2 C) g^(1)(x) = 1/2x  2 D) g^(1)(x) = 2x  4 I *think* it might be C but …