If f ( x ) = 9 x + 3 9 x for all x ∈ R then the sum f ( 1996 1 ) + f ( 1996 2 ) + …… .. + f ( 1996 1995 ) is

f ( x ) = 9 x + 3 9 x ⇒ f ( 1 − x ) = 3 + 3 x 3 ∴ f ( x ) + f ( x ) = 1

Start Free Mock LoginAlready registered? Login here

Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsFunctional EquationMedium2 minQB

MathematicsMediumsingle choice

If $f (x) = \frac{9 ^{x}}{9 ^{x} + 3}$ for all $x \in R$ then the sum $f (\frac{1}{1996}) + f (\frac{2}{1996}) + \dots\dots .. + f (\frac{1995}{1996})$ is

Options:

Answer:

Solution:

$f (x) = \frac{9 x}{9 ^{x} + 3} \Rightarrow f (1 - x) = \frac{3}{3 + 3 ^{x}} ∴ f (x) + f (x) = 1$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Functional Equation

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...