Question

Let $f$ and $g$ be differential functions satisfying $g^{\prime }\left(a\right)=2,g\left(a\right)b$ and $fog=I$ (identify function) then $f^{\prime }\left(b\right)=$ :

• A. $1/2$
• B. $2$
• C. $2/3$
• D. None of these

Answer 1

Answer: (A)

$1/2$

$fog=I\Rightarrow fog\left(x\right)=x\forall x$
$\Rightarrow f^{\prime }\left(g\right(x\left)\right)g^{\prime }\left(x\right)=1\forall x$
$\Rightarrow f^{\prime }\left(g\right(a\left)\right)=\frac{1}{g^{\prime }\left(a\right)}=\frac{1}{2}\Rightarrow f^{\prime }\left(b\right)=\frac{1}{2}$