Find the minimum value of \(9^x - 3^x + 1\) over all real numbers x.
Let 3^x = m .....so........(3^x)^2 = (3^2)^x = m^2 = (9)^x
So we have
m^2 - m + 1 complete the square on m
m^2 - m + 1/4 + 1 - 1/4
(m - 1/2)^2 + 3/4
And this will be a minimum of 3/4 when m = 1/2
