Question

If x Ī R, then the expression 9^x – 3^x + 1 assumes –

• A. All real values
• B. All real values greater than 0
• C. All real values greater than ¾
• D. All real values greater than ¼

Answer 1

Answer: (C)

All real values greater than ¾

Answer 2

f(x) = 9^x – 3^x + 1 = 3^2x – 3^x + $\frac{1}{4}$ + $\frac{3}{4}$

= $\left( 3^{x} - \frac{1}{2} \right)^{2}$ + $\frac{3}{4}$ >$\frac{3}{4}$