- Home
- Standard 12
- Mathematics
1.Relation and Function
normal
If the function $f(x) = x^5 + e^{\frac {x}{5}}$ and $g(x) = f^{-1} (x)$ , then the value of $\frac{1}{{g'\left( {1 + {e^{1/5}}} \right)}}$ is
A
$5$
B
$5 + \frac{{{e^{1/5}}}}{5}$
C
$1$
D
$5 + \frac{5}{e}$
Solution
we have ${x^5} + {e^{x/5}} = 1 + {e^{1/5}}$
$\Rightarrow f(x)=5 x^{4}+\frac{1}{5} e^{x / 5}=5+\frac{1}{5} e^{1 / 5}$
$\Rightarrow \quad x=1, f(x)=5+\frac{1}{5} e^{1 / 5}$
use $g^{\prime}(y)=\frac{1}{f^{\prime}(x)}$
$\Rightarrow g^{\prime}\left(1+e^{1 / 5}\right)=\frac{1}{f^{\prime}(1)}=\frac{1}{5+\frac{e^{1 / 5}}{5}}$
Standard 12
Mathematics
