Doubt From Definite Integration

(a)-(0,\infty)

(b)- 6ln2

(c)-126

Isn't f(x) a constant function?

Can u hint me how to find the function using the functional relation give ......?

Consider g(x) = \dfrac{f(x)}{3}

Then we have g(x+y) = g(x) g(y)

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partial differentiated and find value of
f(x)=3{2^{x}}
sorry for late reply not active in forum little busy now a days..

But this does not satisfy the given relation

r u telling me?? @Samrat_2020 mine fx is satisfying

Can u please show the working of the partial diff method din't get it........
@Sneha_2021

Isn't

f(x+y)=f(x)f(y)
f(x)=a^x isnt it so??

Yeah but there is a 3

Never mind it was my mistake understood it now

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Thanks ! Got it
@Snehal_Agrawal1

Jst a confirmation.......can this partial doff method be used as a general procedure to dermine f(x) pf any functional relation or its specific

mostly when all are product of unkown functions

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