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General Tips for Choosing Function

For real numb...

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For real numbers x and y, the relation f satisfies f(xy) = f(x).f(y) and f(0)≠0. Find the value of f(2019).

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f : [0, 1] \to R

f (x y) = f (x) . f (y)

\in

f (0) \neq 0

y = y (x)

satisfies the differential equation ,

\frac{d y}{d x} = f (x)

y (0) = 1

y (\frac{1}{4}) + y (\frac{3}{4})

Q. Find the natural number

a

\sum_{k = 1}^{n} f (a + k) = 16 (2^{n} - 1)

where the function

f

satisfies the relation

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

for all natural numbers

x, y

f (1) = 2

f

be a function satisfying

f (x y) = \frac{f (x)}{y}

for all positive real numbers

x

y

f (30) = 20

, then the value of

f (40)

f : Z \to Z

be a function satisfying

f (0) \neq 0, f (1) = 0

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

;

(\begin{matrix} f (x - y) - f (0) \end{matrix}) f (x) f (y) = 0

x, y, \in Z

, simultaneously.
(a) Find the set of all possible values of the function

f

f (10) \neq 0 a n d f (2) = 0

, find the set of all integers

n

f (n) \neq 0

f : R^{+} \to R^{+}

be a function satisfying the relation \(f(x.f(y))=f(xy)+x~for~all~x,y \epsilon R^{+}\). Then

l i m x \to 0 (\frac{(f (x))^{\frac{1}{3}} - 1}{(f (x))^{\frac{1}{2}} - 1})

=

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