If g is the inverse of a function f and `f'(x) = 1/(1+x^(5))`, then g'(x) is equal to
Text Solution
AI Generated Solution
To find \( g'(x) \) where \( g \) is the inverse of the function \( f \) and \( f'(x) = \frac{1}{1+x^5} \), we can follow these steps:
### Step 1: Understand the relationship between \( f \) and \( g \)
Since \( g \) is the inverse of \( f \), we have:
\[
f(g(x)) = x
\]
...
Topper's Solved these Questions
PROBABILITY
JEE MAINS PREVIOUS YEAR ENGLISH|Exercise All Questions|11 Videos
SEQUENCES AND SERIES
JEE MAINS PREVIOUS YEAR ENGLISH|Exercise All Questions|10 Videos
Similar Questions
Explore conceptually related problems
Consider a function f(x)=x^(x), AA x in [1, oo) . If g(x) is the inverse function of f(x) , then the value of g'(4) is equal to
Let g be the inverse function of f and f'(x)=(x^(10))/(1+x^(2)). If g(2)=a then g'(2) is equal to
Let g be the inverse function of f and f'(x)=(x^(10))/(1+x^(2)). If f(2)=a then g'(2) is equal to
If g is the inverse function of and f'(x) = sin x then prove that g'(x) = cosec (g(x))
If f(x)=x^(3)+3x+1 and g(x) is the inverse function of f(x), then the value of g'(5) is equal to
Consider the function f(x)=tan^(-1){(3x-2)/(3+2x)}, AA x ge 0. If g(x) is the inverse function of f(x) , then the value of g'((pi)/(4)) is equal to
Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^(3)) .Find g'(x) in terms of g(x).
If e^f(x)= log x and g(x) is the inverse function of f(x), then g'(x) is
If f(x) = 3x + 1 and g(x) = x^(2) - 1 , then (f + g) (x) is equal to
Let g (x) be then inverse of f (x) such that f '(x) =(1)/(1+ x ^(5)), then (d^(2) (g (x)))/(dx ^(2)) is equal to:
JEE MAINS PREVIOUS YEAR ENGLISH-RELATIONS AND FUNCTIONS-All Questions
