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1.Relation and Function
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જો $f\left( x \right) = {\left( {2x - 3\pi } \right)^5} + \frac{4}{3}x + \cos x$ અને $g$ એ $f$ નુ પ્રતિવિધેય હોય તો $g'\left( {2\pi } \right)$ = ?
A
$\frac{7}{3}$
B
$\frac{3}{7}$
C
$\frac{{30{\pi ^4} + 4}}{3}$
D
$\frac{3}{{30{\pi ^4} + 4}}$
Solution
$g(x)=f^{-1}(x)$
$g(f(x))=x$
$g^{\prime}(f(x)) f^{\prime}(x)=1$
Put $x=\frac{3 \pi}{2}$
$g^{\prime}(2 \pi) \cdot f^{\prime}\left(\frac{3 \pi}{2}\right)=1$
$g^{\prime}(2 \pi)=3 / 7$
Standard 12
Mathematics
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