Question

Calculate g(b) and g′(b), where g is the inverse of f.
f(x) = x+sin(x), b = 0

Answer 1

\[f(0)=0\] so
\[g(0)=0\] as well

Answer 2

\[g'(0)=\frac{1}{f'(g(0))}=\frac{1}{f'(0)}\] so find
\[f'(x)\] then
\[f'(0)\] and then take the reciprocal

Answer 3

Thanks a bunch, I just have a hard time just realizing this stuff. You think you could tell me what I should be looking for with these type of questions?