Functions

[cypherskull]

f is a real valued function such that f(x) - 3f(72/x) = 4x (x not equal to 0). Find the value of f(3).

a. -52/3
b. -75/2
c. -15/4
d. -78/9

[Anurag@Gurome]

f is a real valued function such that f(x) - 3f(72/x) = 4x (x not equal to 0). Find the value of f(3)

f(x) - 3f(72/x) = 4x ............................................................... (A)
Replacing x with 72/x ---> f(72/x) - 3f(x) = 4*(72/x) = 288/x ............. (B)

Multiplying (B) with 3 and adding that with (A), we have..
--> f(x) - 9f(x) = 4x + 3*(288/x)
--> f(x) = -(4x + 3*(288/x))/8

Hence, f(3) = -(4*3 + 3*(288/3))/8 = -(12 + 288)/8 = -300/8 = -75/2

The correct answer is B.