If g is the inverse of a function f and f^(')x=1/(1+x^5), then g^(')x is equal to

Correct answer: (B) 1+gx^5. g is the inverse of f i.e. gx=f^(-1)x ⇒fgx=x Differentiating both the sides w.r.t x , we get f^(')gx.g^(')x=1 ⇒g^(')x=1/(f^(')gx)as f^(')x=1/(1+x^5) ⇒g^(')x=1/(11+gx^5) g^(')x=1+gx^5

Q41 / 90 · JEE Main 2014 (06 Apr) · Mathematics

If $g$ is the inverse of a function $f$ and $f^{'} (x) = \frac{1}{1 + x^{5}},$ then $g^{'} (x)$ is equal to

A
$\frac{1}{1 + {\{g (x)\}}^{5}}$
Correct answer
B
$1 + {\{g (x)\}}^{5}$
C
$1 + x^{5}$
D
$5 x^{4}$

Solution

$g$ is the inverse of $f$ i.e. $g (x) = f^{- 1} (x)$

$\Rightarrow f (g (x)) = x$

Differentiating both the sides w.r.t $x$ , we get

$f^{'} (g (x)) . g^{'} (x) = 1$

$\Rightarrow g^{'} (x) = \frac{1}{f^{'} (g (x))}$ as $(f^{'} (x) = \frac{1}{1 + x^{5}})$

$\Rightarrow g^{'} (x) = \frac{1}{(\frac{1}{1 + {(g (x))}^{5}})}$

$g^{'} (x) = 1 + {(g (x))}^{5}$

Hence, the correct answer is option: 'B'.

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If g is the inverse of a function f and f'x=11+x5, then g'x is equal to

Solution

Relevant Questions

If $g$ is the inverse of a function $f$ and $f^{'} (x) = \frac{1}{1 + x^{5}},$ then $g^{'} (x)$ is equal to