Question

I need help with #'s 59, 63, 67, and 71 PLEASE!!!I need to find the domain!!​

Answer 1

9514 1404 393

Answer:

  59.  t ≥ -1

  63.  x ≤ -1/2

  67.  (x ≤ 0) ∪ (x ≥ 6)

  71.  x > 1/2

Step-by-step 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.

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59. t+1 ≥ 0   ⇒   t ≥ -1

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63. 1 -2x ≥ 0   ⇒  x ≤ -1/2

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67. x² -6x ≥ 0   ⇒   x(x -6) ≥ 0   ⇒   (x ≤ 0) ∪ (x ≥ 6)

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71. 2x -1 > 0   ⇒   x > 1/2 . . . . note we left off the =0 case for this one

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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.