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The range of the function ƒ(x)=8 x +4 x +8 -x +4 -x +5 is

The range of the function


ƒ(x)=8x+4x+8-x+4-x+5  is

Grade:12

1 Answers

Pratham Ashish
17 Points
13 years ago

hi,

 you can see that ,

                   ƒ(x)= ƒ(-x)

it indicates that our graph is symmetrical  on both sides ofy- axis, so analysis of function on any of the side will be enough,  we will take care of only +x axis.....

  ƒ(x)=8x+4x+8-x+4-x+5   ,

on diff. w.r.t x

d/df  ƒ(x)  =  ln 8 .8x + ln 4 .4- ln8 8-x  - ln4 4-x 

                = ln8 ( 8x - 8-x )   +  ln 4 (  .4- 4-x )

we know that if  A > 1 than A -1/A   will always be >0

so , ( 8x - 8-x )    &  ( 4- 4-x )  will always be >0

so,  ln8 ( 8x - 8-x )   +  ln 4 (  .4- 4-x )    >0    for    x  >0       ( remind that we are taking care of only  +x axis )

it shows that df/dx is always >o  for x >o

means the min value would be at x =0 

                              min. f   = f (o) =  9

& its obvious that the max. value of F(X) is  infinity

  range of f(x) =  [ 9 ,∞) 

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