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Grade 12Differential Calculus

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)

Profile image of MEGHMA CHAKRABORTY
9 Years agoGrade 12
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1 Answer

Profile image of Vikas TU
9 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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