If $x \in R,$then the expression $9^x-3^x+1$ assumes

Since the function $f\left(x\right)=9^x-3^x+1$ is continuous for all $x$and every continuous function attains every value between its maximum and minimum values. Therefore,$f\left(x\right)$ takes every value between its minimum and maximum values. We have

$f\left(x\right)=9^x-3^x+1={\left(3^x-\frac{1}{2}\right)}^2+\frac{3}{4}>\frac{3}{4}$ for all $x$

Thus,$f\left(x\right)$ assumes all real values greater than $3 / 4$.