Let f:  \to  be a function such that f(x+y)=f(x)+f(y) for all x, y \in , and g: (0, \infty) be a function such that g(x+y)=g(x) g(y) for all x, y \in . If f (\frac{-3}{5}) =12 and g (\frac{-1}{3}) =2, then the value of (f (\frac{1}{4}) +g(-2)-8) g(0) is _______. [JEE Adv 2024 P2]

Functions

Section: Mathematics

Question : 5 of 30

Marks: +1, -0

Let f: →  be a function such that f(x+y)=f(x)+f(y) for all x,y∈ , and g: (0,∞) be a function such that g(x+y)=g(x)g(y) for all x,y∈ . If f(‌

−3

)=12 and g(‌

−1

)=2, then the value of (f(‌

)+g(−2)−8)g(0) is _______.

[JEE Adv 2024 P2]

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