This is a Test of Mathematics Solution Subjective 64 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East-West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
If f(x) is a real-valued function of a real variable x, such that 2f(x) + 3f(-x) = 15 – 4x for all x, find the function f(x).
2f(x) + 3f(-x) = 15 – 4x
Putting x =0, we gets
2f(0) + 3f(0) = 15
Or, f(0) = 3.
Let g(x) = f (x) – 3
2f(x) + 3f(-x) = 15 – 4x
Or, 2g(x) + 3g(-x) = - 4x …(i)
Now put x = - x
2g(-x) + 3g(x) = 4x …(ii)
(i) + (ii), g(x) + g(-x) = o
Or, g(x) = -g(-x) …(iii)
Now 2g(x) + 3g(-x) = - 4x
Or, –g(x) = - 4x [from (iii)]
Or, g(x) = 4x
Or, f(x) = 4x + 3
This is a Test of Mathematics Solution Subjective 64 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East-West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
If f(x) is a real-valued function of a real variable x, such that 2f(x) + 3f(-x) = 15 – 4x for all x, find the function f(x).
2f(x) + 3f(-x) = 15 – 4x
Putting x =0, we gets
2f(0) + 3f(0) = 15
Or, f(0) = 3.
Let g(x) = f (x) – 3
2f(x) + 3f(-x) = 15 – 4x
Or, 2g(x) + 3g(-x) = - 4x …(i)
Now put x = - x
2g(-x) + 3g(x) = 4x …(ii)
(i) + (ii), g(x) + g(-x) = o
Or, g(x) = -g(-x) …(iii)
Now 2g(x) + 3g(-x) = - 4x
Or, –g(x) = - 4x [from (iii)]
Or, g(x) = 4x
Or, f(x) = 4x + 3
