Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Find the function f(x) which is differentiable and satisfy the relation    <img alt="f(x+y)=f(x)+f(y)+(e^x-1)(e^y-1) \forall x,y\epsilon R\\" src="https://entrancecorner.on

Find the function f(x) which is differentiable and satisfy the relation   

f(x+y)=f(x)+f(y)+(e^x-1)(e^y-1) \forall x,y\epsilon R\\ and f'(0)=2

Option: 1

f(x)=e^x+x+1


Option: 2

f(x)=e^x+x


Option: 3

f(x)=e^x+x-1


Option: 4

None of these


Answers (1)

\\f(x+y)=f(x)+f(y)+(e^x-1)(e^y-1) \forall x,y\epsilon R\\ \text{differentiate w.r.t x, keeping y as constant, we get}\\ f'(x+y)=f'(x)+e^x(e^y-1)\\ \text{put x=0}\\ f'(y)=f'(0)+(e^y-1)\\ f'(y)=2+e^y-1\\ f(y)=e^y+y+c\\ \text{Now put x=y=0 in original equation }\\ f(0)=f(0)+f(0)+0\\ f(0)=0\\ \text{put y=0 in}f(y)=e^y+y+c\\ c=-1\\ f(x)=e^x+x-1

Posted by

Kshitij

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question