Let f and g be differentiable functions on R
such that fog is the identity function. If for some
a, b \[ \in \] R, g'(a) = 5 and g(a) = b, then f'(b) is
equal to :
Solutions · 1
Official solution
Given the function composition f(g(x)) is the identity function, it means f(g(x)) = x for all x.
\[ \Rightarrow \] f'(g(x)) g'(x) = 1
put x = a
\[ \Rightarrow \] f'(b) g'(a) = 1
\[ \Rightarrow \] f'(b) = \[{1 \over 5}\]