Home
Class 12
MATHS
if f(x)=x^(2)x,x in (1,infty) and g(x) b...

if `f(x)=x^(2)x,x in (1,infty)` and `g(x)` be inverse function of `f(x)` then `g^(')(x)` must be equal to

A

`(1)/(x(1+l n (g(x))))`

B

`(1)/(x(1+l nx))`

C

`(1)/(g(x).(1+l n (g(x)))`

D

non existent

Text Solution

Verified by Experts

The correct Answer is:
A
We have `f(g(x))=g(x)^(g(x))=x`
also `g(f(x))=x`
`impliesg^(')(f(x)).f'(x)=1impliesg^(')(f(x))=(1)/(f'(x))`
`impliesg^(')(f(x))=(1)/(x^(x).(1+l n x))`
`impliesg^(')(f(g(x)))=(1)/((g(x))^(g(x)).(1+l n (g(x))))`
`impliesg^(')(x)=(1)/(x(1+l n g(x)))`
Promotional Banner

Similar Questions

Explore conceptually related problems

If ef(x)=log x and g(x) is the inverse function of f(x), then g'(x) is

If g(x) is inverse function of f(x)=x^(3)+3x-3 then g'(1)=

f(x)=x^(x),x in(0,oo) and let g(x) be inverse of f(x), then g(x) 'must be

If f(x)=x+tanx and g(x) is inverse of f(x) then g^(')(x) is equal to

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

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

f:RtoR is defined as f(x)=x^(3)+2x^(2)+7x+cos(pix) and g be the inverse of function f(x) then g(9) is equal to

Let f(x)=log_(e)x+2x^(3)+3x^(5), where x>0 and g(x) is the inverse function of f(x) , then g'(5) is equal to: