If f and g are two differentiable functions satisfying g1(5)= 34, g(5) = 6 and g=f -1 then the value of f1(6) is equal to …

∵g=f−1;g(5)=6;g1(5)=34⇒f(g(x))=xf1(g(x)).g1(x)=1Put x = 5f1(g(5)).g1(5)=1f1(6).34=1⇒f1(6)=43

If f and g are two differentiable functions satisfying g1(5)= 34, g(5) = 6 and g=f -1 then the value of f1(6) is equal to …

∵g=f−1;g(5)=6;g1(5)=34⇒f(g(x))=xf1(g(x)).g1(x)=1Put x = 5f1(g(5)).g1(5)=1f1(6).34=1⇒f1(6)=43

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If f and g are two differentiable functions satisfying g¹(5)= $\frac{3}{4}$ , g(5) = 6 and g=f ^-1 then the value of f¹(6) is equal to …

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$\frac{3}{4}$

$\frac{1}{4}$

$\frac{4}{3}$

$\frac{1}{6}$

answer is C.

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Detailed Solution

$∵ g = f^{- 1}; g (5) = 6; g^{1} (5) = \frac{3}{4}$

$\begin{array}{l} \Rightarrow f (g (x)) = x \\ f^{1} (g (x)) . g^{1} (x) = 1 \\ P u t x = 5 \\ f^{1} (g (5)) . g^{1} (5) = 1 \\ f^{1} (6) . (\frac{3}{4}) = 1 \Rightarrow f^{1} (6) = \frac{4}{3} \end{array}$

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If f and g are two differentiable functions satisfying g¹(5)= $\frac{3}{4}$ , g(5) = 6 and g=f ^-1 then the value of f¹(6) is equal to …