If f(x) = e^x - Int[0, 1] e^(1-x) (f(x)) dx, prove that f(x)=e^x -1

[GeorgieB]

If f(x) is a continuous function so that
[h=2] f(x)=e^x - Integral[0, 1]e^(1-x) (f(x))dx[/h]proove that f(x)=e^x -1 for every xΕR


thanks in advance!

 

[Steven G]

If f(x) is a continuous function so that
f(x)=e^x - Integral[0, 1]e^(1-x) (f(x))dx

proove that f(x)=e^x -1 for every xΕR


thanks in advance!

Exactly where are you stuck? Show us your work so we can see where you are making your mistakes so we can help you. Thanks.

Also are you sure that you want to prove that f(x) = e^x-1 as you wrote??

 

[GeorgieB]

Exactly where are you stuck? Show us your work so we can see where you are making your mistakes so we can help you. Thanks.

Also are you sure that you want to prove that f(x) = e^x-1 as you wrote??

this is as far as I've gotten and can't really think of anything else.Yes it says proove that f(x)=e^x -1 for every xΕR

 

[Steven G]

View attachment 9480 this is as far as I've gotten and can't really think of anything else.Yes it says proove that f(x)=e^x -1 for every xΕR

Why not plug in e^x - 1 for both f(x) and see if the equal sign is valid. Hint: If you plug in e^x - 1 in the left hand side for f(x), the left hand side will be e^x - 1. Now you plug in e^x - 1 in the right hand side for f(x) and simplify everything and see if you get e^x - 1.

If you do, then you're done. Otherwise you made a mistake somewhere or as I suggested in my last post you have a typo in the original equation.

 

[GeorgieB]

Why not plug in e^x - 1 for both f(x) and see if the equal sign is valid.

The format of my exam does not allow you to use anything from the actual question for your answer so I cannot plug e^x -1 in f(x)

Thank you for your help!