How do you find the inverse of functions? for example how would you find the inverse of y= log8 x

Answer 1

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.

Answer 2

Ok that's slightly confusing.
I understand the flipping of x and y but then what do you do?
so x=log8 y
?

Answer 3

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.}

Answer 4

8^x = 8^log8(y) = y
Simplify and solve y in terms of x.

Answer 5

MMMMmmmmmmk that helps, thanks!

Answer 6

You're welcome!