Relations and Functions (Class 12) · Question 5

Let f: R R be a function such that f(x+y)=f(x)+f(y) for all x,y R, and g: R (0, ) be a function such that g(x+y)=g(x)g(y) for all x,y R. If f ( -35 )=12 and g ( -13 )=2, then the value of (f ( 14 )+g(-2)-8 )g(0) is .

Answer

51

Solution

From the equations: f(rx)=rf(x) for rational r, and g(rx)=g(x)r, g(0)=1.

f(1)=- 53 12=-20, so f ( 14 )=-5.

g(-2)=g (- 13 )6=26=64.

Value =(-5+64-8) 1=51.

Answer: 51