First slide

Differentiability

Question

$Let f and g be differentiable functions such that f o g = I, the identity function,$ $If g^{'} (a) = 2 and g (a) = b, then f (b) =$

Moderate

A

$- 2$
B

$\frac{1}{2}$
C

2
D

None

Solution

$\begin{array}{l} (f o g)' (x) = x f o r a l l x \\ \Rightarrow (f o g)' (a) = 1 \Rightarrow f (g (a)) g' (a) = 1 \\ \Rightarrow f (b) g' (a) = 1 \Rightarrow 2 f (b) = 1 \\ \Rightarrow f (b) = \frac{1}{2} . \\ H e n c e (2) i s t h e c o r r e c t a n s w e r . \end{array}$

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