Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b ϵ R, g'(a) = 5 and g'(a)=b, then f '(b) is equal to :

Question

Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b ϵ R, g'(a) = 5 and g'(a)=b, then f '(b) is equal to : (A) (2/5) (B) 5 (C) 1 (D) (1/5)

Tardigrade Admin · Accepted Answer

Æ(g(x)) = x Æ'(g(x)) g'(x) = 1 put x = a ⇒ Æ'(b) g'(a) = 1 Æ'(b) = (1/5)

Q. Let $f$ and $g$ be differentiable functions on $R$ such that $f o g$ is the identity function. If for some $a, b ϵ R, g^{'} (a) = 5$ and $g^{'} (a) = b,$ then $f^{'} (b)$ is equal to :

$\frac{2}{5}$

$5$

$1$

$\frac{1}{5}$

$ƒ (g (x)) = x$
$ƒ^{'} (g (x)) g^{'} (x) = 1$
put $x = a$
$\Rightarrow ƒ^{'} (b) g^{'} (a) = 1$
$ƒ^{'} (b) = \frac{1}{5}$

Q. Let f and g be differentiable functions on R such that fog is the identity function. If for some a,bϵR,g′(a)=5 and g′(a)=b, then f′(b) is equal to :

52​

5

1

51​

ƒ(g(x))=x ƒ′(g(x))g′(x)=1 put x=a ⇒ƒ′(b)g′(a)=1 ƒ′(b)=51​

Q. Let $f$ and $g$ be differentiable functions on $R$ such that $f o g$ is the identity function. If for some $a, b ϵ R, g^{'} (a) = 5$ and $g^{'} (a) = b,$ then $f^{'} (b)$ is equal to :

$\frac{2}{5}$

$5$

$1$

$\frac{1}{5}$

$ƒ (g (x)) = x$
$ƒ^{'} (g (x)) g^{'} (x) = 1$
put $x = a$
$\Rightarrow ƒ^{'} (b) g^{'} (a) = 1$
$ƒ^{'} (b) = \frac{1}{5}$