Answer
$\begin{array}{llll}
a. & 0 & e. & -\sqrt{x^{2}+x}\\
b. & \sqrt{2} & f. & \sqrt{x^{2}+3x+2}\\
c. & 0 & g. & \sqrt{4x^{2}+2x}\\
d. & \sqrt{x^{2}-x} & h. & \sqrt{x^{2}+2xh+h^{2}+x+h}
\end{array}$
Work Step by Step
$f(x)=\sqrt{x^{2}+x}$
$\begin{array}{lll}
(a)\ f(0) & (b)\ f(1) & (c)\ f(-1)\quad \\
=\sqrt{0^{2}+0} & =\sqrt{1^{2}+1} & =\sqrt{(-1)^{2}+(-1)}\\
=0 & =\sqrt{2} & =\sqrt{1-1}\\
& & =0
\end{array}$
$\begin{array}{ll}
(d)\ f(-x) & (e)\ -f(x)\\
=\sqrt{(-x)^{2}+(-x)} & =-(\sqrt{x^{2}+x})\\
=\sqrt{x^{2}-x}\quad & =-\sqrt{x^{2}+x}\\
&
\end{array}$
$\begin{array}{ll}
(f)\ f(x+1) & (g)\ f(2x)\\
=\sqrt{(x+1)^{2}+(x+1)} & =\sqrt{(2x)^{2}+2x}\\
=\sqrt{x^{2}+2x+1+x+1} & =\sqrt{4x^{2}+2x}\\
=\sqrt{x^{2}+3x+2} & \\
& \\
&
\end{array}$
$(h)\ f(x+h)=\sqrt{(x+h)^{2}+(x+h)}=\sqrt{x^{2}+2xh+h^{2}+x+h}$
