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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
Let $f$ and $g$ be differentiable functions on $\mathrm{R}$ such that $fog$ is the identity function. If for some $a, b \in \mathrm{R}, g^{\prime}(a)=5$ and $g(a)=b,$ then $f^{\prime}(b)$ is equal to
  • A
    $\frac{2}{5}$
  • B
    $1$
  • ✓
    $\frac{1}{5}$
  • D
    $5$
✓

Answer

Correct option: C.
$\frac{1}{5}$
c
$f(g(x))=x$

$f^{\prime}(g(x)) g^{\prime}(x)=1$

put $x=a$ $\Rightarrow f^{\prime}(b) g^{\prime}(a)=1$

$f^{\prime}(b)=\frac{1}{5}$

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