Find the largest possible domain for the following function and state the corresponding range.

$f\left(x\right)=2^x$

Find the largest possible domain for the following function and state the corresponding range.

$f\left(x\right)=\frac{1}{x}$

Find the largest possible domain for the following function and state the corresponding range.

$f\left(x\right)=1/x-2$

Find the largest possible domain for the following function and state the corresponding range.

$f\left(x\right)=\sqrt{x-3}-2$

If $f\left(x\right)=x^2+6$for $x\in \mathrm{ℝ}$ and $g\left(x\right)=\sqrt{x+3}-2$ for $x\in \mathrm{ℝ},x\ge -3$, then find $fg\left(6\right)$.

If $f\left(x\right)=x^2+6$for $x\in \mathrm{ℝ}$ and $g\left(x\right)=\sqrt{x+3}-2$ for $x\in \mathrm{ℝ},x\ge -3$, then find $gf\left(4\right)$.

If $f\left(x\right)=x^2+6$for $x\in \mathrm{ℝ}$ and $g\left(x\right)=\sqrt{x+3}-2$ for $x\in \mathrm{ℝ},x\ge -3$, then find $ff\left(-3\right)$.

$h:x\mapsto x+5$ for $x\in \mathrm{ℝ},x>0$   and  $k:x\mapsto \sqrt{x}$ for $x\in \mathrm{ℝ},x>0$

Express each of the following in terms of $h$ and / or $k$.

$x\mapsto \sqrt{x}+5$

$h:x\mapsto x+5$ for $x\in \mathrm{ℝ},x>0$   and  $k:x\mapsto \sqrt{x }$ for $x\in \mathrm{ℝ},x>0$

Express each of the following in terms of h or k.

$x\mapsto \sqrt{x+5}$