Expressing x in Terms of y, to Find the Range of a Function

Q. If $x$ is real, then the value of the expression $\frac{x^2+14x+9}{x^2+2x+3}$ lies between

1. $4$ and $5$
2. $-4$ and $5$
3. $-5$ and $4$
4. None of these

Q. The range of the function f(x) $=\frac{x-2}{2-x}$ when x $\ne$ 2 is

1. R
2. R - {1}
3. {-1}
4. R-{-1}

Q. The range of the function $f\left(x\right)=[x-9]-(x-3)$ is

1. $(-7,-6]$
2. $[-7,-6]$
3. $(-7,-6)$
4. $[-7,-6)$

Q. Range of the function defined by $9^x+3^{f\left(x\right)}=3$ is :

1. $(-\infty ,1)$
2. $(-1,1)$
3. $(-\infty ,\frac{1}{2})$
4. $(-\infty ,1)\cup (1,\infty )$