Let f(x)=2 x+ex-e-x and g(x) is inverse of f(x), then g prime(x) is

Question

Let f(x)=2 x+ex-e-x and g(x) is inverse of f(x), then g prime(x) is (A) (1/2+√(2 g(x)-x)2-4) (B) (1/2-√(2 g(x)-x)2+4) (C) (1/2+√(2 g(x)-x)2+4) (D) None of these

Tardigrade Admin · Accepted Answer

g prime(f(x))=(1/2+ex+e-x)=(1/2+√(ex-e-x)2+4) x arrow g(x) g prime(x)=(1/2+√(x-2 g(x))2+4)

Q. Let $f (x) = 2 x + e^{x} - e^{- x}$ and $g (x)$ is inverse of $f (x)$ , then $g^{'} (x)$ is

$\frac{1}{2 + ( 2 g ( x ) - x ) ^{2} - 4}$

$\frac{1}{2 - ( 2 g ( x ) - x ) ^{2} + 4}$

$\frac{1}{2 + ( 2 g ( x ) - x ) ^{2} + 4}$

None of these

$g^{'} (f (x)) = \frac{1}{2 + e ^{x} + e ^{- x}} = \frac{1}{2 + ( e ^{x} - e ^{- x} ) ^{2} + 4}$
$x \to g (x)$
$g^{'} (x) = \frac{1}{2 + ( x - 2 g ( x ) ) ^{2} + 4}$

Q. Let f(x)=2x+ex−e−x and g(x) is inverse of f(x), then g′(x) is

2+(2g(x)−x)2−4​1​

2−(2g(x)−x)2+4​1​

2+(2g(x)−x)2+4​1​