Range-of-function-f-x-6-x-3-x-6-x-3-x-2-

Question Number 31865 by rahul 19 last updated on 16/Mar/18

R a n g e o f f u n c t i o n :

f (x) = 6^{x} + 3^{x} + 6^{- x} + 3^{- x} + 2 .

Commented by rahul 19 last updated on 16/Mar/18

m y t r y :

f (x) = {(6^{\frac{x}{2}} + 6^{\frac{- x}{2}})}^{2} + {(3^{\frac{x}{2}} + 3^{\frac{- x}{2}})}^{2} - 2 ⩾ 6 .

h e n c e r a n g e i s [- 6, \infty) .

Commented by rahul 19 last updated on 16/Mar/18

b u t a n s . g i v e n i s [6, \infty) .

Commented by Tinkutara last updated on 16/Mar/18

Apply AM-GM.

Commented by rahul 19 last updated on 16/Mar/18

p l z t e l l w h e r e a m i w r o n g ?

Commented by Tinkutara last updated on 16/Mar/18

B e c a u s e y o u a s s u m e d m i n i m u m

v a l u e o f 6^{\frac{x}{2}} + 6^{\frac{- x}{2}} t o b e 0 w h i c h i s n o t .

6^{\frac{x}{2}} + 6^{\frac{- x}{2}} h a s m i n i m u m v a l u e 2 .

Commented by rahul 19 last updated on 16/Mar/18

o k t h a n k s!!

Answered by mrW2 last updated on 16/Mar/18

f (x) = (6^{x} + 6^{- x}) + (3^{x} + 3^{- x}) + 2

⩾ 2 + 2 + 2 = 6

Commented by rahul 19 last updated on 16/Mar/18

y e s s i r, i h a v e g o t t h e a n s .

t h a n k u s i r!