Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
how can we find out f(x)?? if something like f(x+y)=f(x)+f(y) is given and it also say f(1)=2 so now also find f(2)..?? for functional equations watz the procedure to find out f(x)??
Hi,
It is given that f(x+y) =f(x)+f(y) and f(1)=2
so on keeping x=1 and y=0 in the above eqn we get
f(1)=f(1) +f(0) => f(0)=0 now when we keep x=1 and y=1 we get
f(2)=f(1)+f(1) =>f(2)=4
similarly when we calculate f(3) and f(4) we get them as 6 and 8 respectively.On observing the sequence we come to know that
f(x)=2x
put x=y
then f(2x)=2f(x)
so f(0) = 0
given f(1) = 2
so for x=y=1 f(2) = 2f(1) = 4
so f(2) =4
for x= -y
f(x) + f(-x) = 0
so f(-x) = -f(x) so f(x) is odd function
if we take f(x) to be a polynomia function then
f(x) is of form (px)2n+1
for p=2 and n=0 , we have f(x) = 2x which fits in f(0) , f(1) and f(2) .
SO f(x) = 2x
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !