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 ((-3)/5 ) = 12 and g ((-1)/3 ) = 2, then the value of (f (1/4 ) + g(-2) - 8 )g(0) is ________.

Let f : R → R be a function such that f(x+y) = f(x) + f(y)… — JEE Advanced 2024 Mathematics PYQ

JEE Advanced 2024 · Paper 2 · numerical answer

Let

f : \mathbb{R} \to \mathbb{R}

be a function such that

f(x+y) = f(x) + f(y)

for all

x, y \in \mathbb{R}

, and

g : \mathbb{R} \to (0,\infty)

be a function such that

g(x+y) = g(x)g(y)

for all

x, y \in \mathbb{R}

. If

f\!\left(\dfrac{-3}{5}\right) = 12

and

g\!\left(\dfrac{-1}{3}\right) = 2

, then the value of

\left(f\!\left(\dfrac{1}{4}\right) + g(-2) - 8\right)g(0)

is ________.

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Answer: 51

[JEE Advanced 2024 · Paper 2]

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