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Functions question

2024 · Shift 2 · Q25

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PYQ Library
JEE Advanced
Mathematics
Functions
2024 · Shift 2 · Q25

Functions question

2024 · Shift 2 · Q25

JEE AdvancedMathematicsFunctionsNumerical+4 / −1

Let

f: \mathbb{R} \rightarrow \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} \rightarrow(0, \infty)

be a function such that

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

for all

x, y \in \mathbb{R}

. If

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

and

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

, then the value of

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

is

\underline{\hspace{2cm}}

.

Numerical answer

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