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miniimum value of y+1/y =2
hence min values of 4^x+4^-x = 4^x+1/4^x =2
hence min values of 8^x+8^-x = 8^x+1/8^x =2
hence minimum value of (4^x+4^-x) +(8^x+8^-x)+5= 2+2+5 = 9
range of given function is [ 9, infinity)
hence min values of 4^x+4^-x = 4^x+1/4^x =2
hence min values of 8^x+8^-x = 8^x+1/8^x =2
hence minimum value of (4^x+4^-x) +(8^x+8^-x)+5= 2+2+5 = 9
range of given function is [ 9, infinity)
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