anubis01 said:
Homework Statement
1)Find the inverse of a f(x)=1+e^x/1-e^x
2)solve for x when e^ax=ce^bx where a doesn't equal b.
Homework Equations
1)ln(e^x)=x
2)ln(e^x)=x
You realize those are the same equation, don't you?
The Attempt at a Solution
1)
(1+e^x/1-e^x)(1+e^x/1+e^x)=(2+e^x^2/2)
No, that's just bad algebra. [(1+e^x)(1+e^x)= 1+ 2e
x+ e
2x is the numerator and the denominator is 1- e
2x, not "2".0
ln(2+e^x^2/2)= ln2+x^2/ln2
And even if it were correct, ln(A+ B) is not ln(A)+ ln(B).
sqrt(ln2/ln2)=x
I think this is what x comes out to but I'm not sure.
No, it doesn't. The if y= f(x), then x= f
-1 of y so the standard way to find the inverse of y= f(x) is to solve the equation for x. If y= (1+e
x)/(1- e
x) then (1- e
x)y= 1+ e
x or y- ye
x= 1+ e
x. y(1+ e
x)= y- 1, 1+ e
x= (y- 1)/y, e
x= (y-1)/y- 1= (y-1)/y- y/y= -1/y. Can you solve that for x?
2)
ln(e^ax)=ln(ce^bx)
ax=bxC
No, ln(AB) is not A ln(B) ln(ce^(bx))= ln(c)+ ln(bx)= ln(c)+ bx.
a-b=x-x
Again I'm not sure if this is right, any help is much appreciated.
Since the "x"s cancel out in what you have, you should be sure it is not right!