Question

if f(x) = 9^x upon 9^x+3 then f (x) + f ( 1-x)

Answer 1

1 will be the answer..

Answer 2

Given :

The function f ( x ) = $\dfrac{9^{x}}{9^{x+3}}$

To Find :

 f ( x )  +   f ( 1 - x )

Solution :

∵  f ( x ) = $\dfrac{9^{x}}{9^{x+3}}$

Or,   f ( x ) = $9^{ (x) - ( x+3)}$           ( ∵ $\dfrac{a^{b} }{a^{c} }$  =  $a^{b+c}$    , from base indices formula )

i.e   f ( x ) = $9^{ (-3 )}$          ...........1

And,  for x = 1 - x

i.e   f ( 1 - x ) = $\dfrac{9^{1 - x}}{9^{1 - x +3}}$

Or,   f ( 1 - x ) = $\dfrac{9^{1 - x}}{9^{4- x }}$

Or,  f ( 1 - x ) =  $9^{ (1-x) - (4 - x)}$         ( ∵ $\dfrac{a^{b} }{a^{c} }$  =  $a^{b+c}$    , from base indices formula )

Or,  f ( 1 - x ) =  $9^{ (5-2 x )}$           ...........2

Now, From eq 1 and eq 2

  f ( x ) + f ( 1 - x ) =  $9^{ (-3 )}$ + $9^{ (5-2 x )}$  

Hence, The value of   f ( x ) + f ( 1 - x ) is  $9^{ (-3 )}$ + $9^{ (5-2 x )}$     Answer