FIND THE RANGE OF 9^x - 3^x+1

Dear student

y = 9^{x} - 3^{x} + 1 = {(3^{2})}^{x} - 3^{x} + 1 = {(3^{x})}^{2} - 2 \times 3^{x} \times \frac{1}{2} + \frac{1}{4} + \frac{3}{4} = {(3^{x} - \frac{1}{2})}^{2} + \frac{3}{4} y i s l e a s t w h e n t e r m u n d e r s q u a r e 3^{x} - \frac{1}{2} i s z e r o y (m i n) = 3 / 4 y h a s m a x i m u m v a l u e t o i n f i n i t y a s x t e n d s t o i n f i n i t y s o, r a n g e = [3 / 4, \infty)

Regards

FIND THE RANGE OF 9x - 3x +1