1. $\phantom{a}$
1. No
2. Yes
3. No
4. Yes
5. Yes
6. No
7. Yes
8. $y^2=1+x^2$
$y=\pm \sqrt{1+x^2}$
No
9. $\sqrt{y}=2-x$
$y=(2-x)^2$
Yes
10. $y^2=1-x^2$
$y=\pm \sqrt{1-x^2}$
No
2. All real numbers $-\infty, \infty$
3. $\phantom{a}$
$\begin{array}[t]{rrrrr} 5&-&4x&\ge &0 \\ -5&&&&-5 \\ \hline &&\dfrac{-4x}{-4}&\ge &\dfrac{-5}{-4} \\ \\ &&x&\le &\dfrac{5}{4} \\ \end{array}$$\left(-\infty, \dfrac{5}{4}\right]$
4. $t^2\neq 0$
$t\neq \sqrt{0}\text{ or }0$
5. All real or $(-\infty, \infty)$
6. $\phantom{a}$
$\begin{array}[t]{rrrrr} t^2&+&1&\neq &0 \\ &-&1&&-1 \\ \hline &&t^2&\neq &-1 \\ &&t&\neq & i \\ \\ &&t&=&\mathbb{R} \end{array}$
7. $\phantom{a}$
$\begin{array}[t]{rrrrr} x&-&16&\ge &0 \\ &+&16&&+16 \\ \hline &&x&\ge &16 \\ \end{array}$
$[16, \infty)$
8. $x^2-3x-4\neq 0$
$(x-4)(x+1)\neq 0$
$x\neq 4,1$
9. $\phantom{a}$
$\begin{array}[t]{ll} \begin{array}[t]{rrrrr} 3x&-&12&\ge &0 \\ &+&12&&+12 \\ \hline &&\dfrac{3x}{3}&\ge &\dfrac{12}{3} \\ \\ &&x&\ge &4 \end{array} &\hspace{0.25in} \begin{array}[t]{rrl} x^2-25&\neq &0 \\ (x-5)(x+5)&\neq &0 \\ x&\neq &5, -5 \\ \\ \therefore x&\ge &4, \neq \pm 5 \end{array} \end{array}$
10. $g(0)=\cancel{4(0)}-4$
$\phantom{g(0)}=-4$
11. $g(2)=-3\cdot 5^{-2}$
$\phantom{g(2)}=-\dfrac{3}{25}$
12. $f(-9)=(-9)^2+4$
$\phantom{f(-9)}=81+4$
$\phantom{f(-9)}=85$
13. $f(10)=10-3$
$\phantom{f(10)}=7$
14. $f(-2)=3^{-2}-2$
$\phantom{f(-2)}=\dfrac{1}{9}-2$
$\phantom{f(-2)}=\dfrac{1}{9}-\dfrac{18}{9}$
$\phantom{f(-2)}=-\dfrac{17}{9}$
15. $f(2)=-3^{2-1}-3$
$\phantom{f(2)}=-3^1-3$
$\phantom{f(2)}=-6$
16. $k(2)=-2\cdot 4^{2(2)-2}$
$\phantom{k(2)}=-2\cdot 4^{4-2}$
$\phantom{k(2)}=-2\cdot 4^2$
$\phantom{k(2)}=-32$
17. $p(-2)=-2\cdot 4^{2(-2)+1}+1$
$\phantom{p(-2)}=-2\cdot 4^{-4+1}+1$
$\phantom{p(-2)}=-2\cdot 4^{-3}+1$
$\phantom{p(-2)}=-\dfrac{2}{64}+1$
$\phantom{p(-2)}=-\dfrac{1}{32}+1 \Rightarrow \dfrac{-31}{32}$
18. $h(-4x)=(-4x)^3+2$
$\phantom{h(-4x)}=-64x^3+2$
19. $h(n+2)=4(n+2)+2$
$\phantom{h(n+2)}=4n+8+2$
$\phantom{h(n+2)}=4n+10$
20. $h(-1+x)=3(-1+x)+2$
$\phantom{h(-1+x)}=-3+3x+2$
$\phantom{h(-1+x)}=3x-1$
21. $h(\dfrac{1}{3})=-3\cdot 2^{\frac{1}{3}+3}$
$\phantom{h(\dfrac{1}{3})}= -2^3\cdot 3\sqrt[3]{2}$
$\phantom{h(\dfrac{1}{3})}=-8\cdot 3\sqrt[3]{2}$
$\phantom{h(\dfrac{1}{3})}=-24 \sqrt[3]{2}$
22. $h(x^4)=(x^4)^2+1$
$\phantom{h(x^4)}=x^8+1$
23. $h(t^2)=(t^2)^2+t$
$\phantom{h(t^2)}=t^4+t$
24. $f(0)=|\cancel{3(0)}+1|+1$
$\phantom{f(0)}=1+1\text{ or }2$
25. $f(-6)=-2 |-(-6)-2 | +1$
$\phantom{f(-6)}=-2 |6-2| + 1$
$\phantom{f(-6)}=-2(4)+1$
$\phantom{f(-6)}=-8 + 1\text{ or }-7$
26. $f(10)=|10+3|$
$\phantom{f(10)}=13$
27. $p(5)=-|5|+1$
$\phantom{p(-5)}=-5+1$
$\phantom{p(-5)}=-4$