Find f of g and g of f if:

f(x)= 1/(2x-1)

g(x)=1-ln(x+1)

How do I solve for x? Is this what I should do? How should I present my answers? Please help!

f of g

1/(2*1-ln(x+1)-1)

1/(2-1-2ln(x+1))

1/(1-ln(x+1)(x+1))

x= -1

g of f

1-ln(1/(2x-1)+1)

1-ln(2x/(2x-1))

1=ln(2x/(2x-1))

e^{1}=2x/(2x-1)

e(2x-1)=2x

2xe-e=2x

2xe-2x=e

x(2e-2)=e

x=e/(2e)

x=1/2