> In Exercises 21-32, find the domain of each function
21. $f(x) = x^3 - 4x + 1$
23. $f(x) = \sqrt{2x^2 - 3x + 1}$
$f(x) = \sqrt{1 - 7x}$
1
24. $f(x) = \frac{1}{\sqrt{x - 5}}$
25. $f(x) = \frac{\sqrt{2x + 1}}{\sqrt{x + 2}}$
26. $f(t) = \sqrt{3 - \frac{1}{t^2}}$
21 - 8
r - 1
27. $g(w) = \frac{2}{w - 1}$
28. $g(t) = \frac{2t - 8}{t^2 - 16}$
29. $g(r) = \frac{r - 1}{r^2 - r - 6}$
2x³ - 3x + 1
2x - 5
3x² + x + 4
30. $f(x) = \frac{2x^3 - 3x + 1}{|2x - 4| + 1}$
31. $f(x) = \frac{2x - 5}{x + 1} - 3$
32. $f(x) = \frac{3x^2 + x + 4}{\sqrt{2x - 4} - 3}$
> In Exercises 33-41, determine all intercepts of the graph of the equation.
33. $x = 3y^2 - 2$
34. $x^2 - y^2 = 1$
35. $x^4 = 3y^3$
36. $x^2y^2 - 2x^3 = 1$
37. $y = x - \frac{1}{x}$
38. $y = \sqrt{9 - x^2}$
39. $y = \frac{1}{3}x$
40. $2x = -y^2$
41. $y = x^2 - 3$
> In Exercises 42-47, determine which of the following functions are odd, even, or neither
$f(x) = 5x^2 - 3$
45
$f(x) = (x^2 + 2)^3$
$f(x) = (x - 2)^2$
y=
[ ]
$f(x) = \frac{x}{x^2 + 4}$
$f(x) = x(x^2 + 1)^3$
> In Exercises 48-56, let $f(x) = x^2 + 4x - 2$ and $g(x) = 2 - x^2$. Find the specified values
8. $(f + g)(-1)$
51. $(f \cdot g)(0)$
54. $(g \circ f)(3)$
$(f - g)(2)$
[ ]
(α)
55. $(f \circ f)(-2)$
50. $(f - g)(a), a \in R$
53. $(f \circ g)(3)$
$(g \circ g)(2)$
