9514 1404 393
Answer:
59. t ≥ -1
63. x ≤ -1/2
67. (x ≤ 0) ∪ (x ≥ 6)
71. x > 1/2
Explanation:
The domain is the set of values of x where the function is defined. In rational functions it excludes any values of x that make the denominator zero. When even-index roots are involved, it excludes values of x that make the argument of the root function negative.
__
59. t+1 ≥ 0 ⇒ t ≥ -1
__
63. 1 -2x ≥ 0 ⇒ x ≤ -1/2
__
67. x² -6x ≥ 0 ⇒ x(x -6) ≥ 0 ⇒ (x ≤ 0) ∪ (x ≥ 6)
__
71. 2x -1 > 0 ⇒ x > 1/2 . . . . note we left off the =0 case for this one
_____
The attachment is a plot of the g(x) in 67. You can see that it is undefined for 0 < x < 6.
As you can see, a graphing calculator can be helpful in identifying the domain. Of course, any vertical asymptotes are excluded, as are any "holes" in a function.