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range of function f(x)= 6 ^x +3 ^x +6 ^-x +3 ^-x +2? a.[-2,infinity) b.(-2,infinity) c.(6,infinity) d.[6,infinity)

 
range of function f(x)= 6^x+3^x+6^-x+3^-x+2?
a.[-2,infinity)  b.(-2,infinity)  c.(6,infinity)  d.[6,infinity)

Grade:12

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
We know for any positive number a , a^x + a^-x  has minimum value of 2
         Here , 6 and 3 both are positive number .
         So, 6^x + 6^-x + 3^x +3^-x has minimum value of 2+2= 4 and upto infinity.
        Therefore  minimum value of the whole function  is 4+2=6
        Ans will be à [6,infinity] .
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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