Question

State true or false:

If $f\left(0\right)=a,f^{\prime }\left(0\right)=b,g\left(0\right)=0$ and $\left(fog{)}^{\prime }\right(0)=c$, then $g^{\prime }\left(0\right)=\frac{c}{b}$

• A. True
• B. False

Answer 1

The correct option is A True

Given$f\left(0\right)=a,f^{\prime }\left(0\right)=b,g\left(0\right)=0$and$\left(fog{)}^{\prime }\right(0)=c$,
$\left(fog{)}^{\prime }\right(0)=c$

$\Rightarrow f^{\prime }\left(g\right(0\left)\right).g^{\prime }\left(0\right)=c$
$\Rightarrow f^{\prime }\left(0\right).g^{\prime }\left(0\right)=c$
$\Rightarrow b.g^{\prime }\left(0\right)=c$

$\Rightarrow \left(g^{\prime }\right(0)=\frac{c}{b}$