find the range of the function

Question

find the range of the function f(x)=6^x+3^x+6^-x+3^-x+2.

hint:- the answer is given [4,infinity) but i cant get the procedure.

Answer 1

if x=0, the first four terms are each equal to 1, so the y = 6.

if x=1, y = 6+3+1/6+1/3+2

if x=-1, y = 1/6+1/3+6+3+2 (same as above).

This 'study' shows me that the range is probably (6,infinity).

 

Further exploration: f(0.1) = 2.03219 (two terms with base 6) + 2.01208 (two terms with base 3) + 2 which is just a bit above y=6.

 

If you have a graphing calculator, I suggest graphing it and using the CALC ability to find the minimum.