MathematicsIf 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 …

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 …

A
$\frac{3}{4}$
B
$\frac{1}{4}$
C
$\frac{4}{3}$
D
$\frac{1}{6}$

Solution:

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

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

Related content

Area of Square

Area of Isosceles Triangle

Pythagoras Theorem

Triangle Formulae

Perimeter of Triangle Formula

Area Formulae

Volume of Cone Formula

Matrices and Determinants_mathematics

Critical Points Solved Examples

Type of relations_mathematics