over which of the following domains is f(x) = csc(0.1x + 1.2) defined at all points and invertible?

Question

x = [0,10]
x = [10,20]
x = [20,30]
x = [30,40]

Can someone please explain how to solve this to me and show me all the steps rather than simply giving me the answer so I can understand it?

Answer 1

the domain must be at most 1/2 period, or 2π/.1 = 20π. In addition, it must not contain an asymptote or a max/min, because there the curve doubles back, so it fails the horizontal-line test.

All of those intervals are short enough, so we need to consider that there is an asymptote at x = 10π-12 ≈ 19.4

there is a min/max where .1x+1.2=π/2 or 3π/2
x ≈ 4 and 34

Looks like [20,30] is the answer.

Answer 2

1. C (28.3)
2. E (sec x)
3. B (tan x and sec x)
4. E (sec x)
5. A (2.5 seconds)
6. D (a=1; b=-1; c=pi)
7. C (f(x)=2sin(-1.5x+0.5)-2)
8. B (theta(t)=6cos(2pi/3 t)
9. C (x=[20,30])
10. A (a decreasing function defined in Quadrants I and II)
11. B (51°)
12. D (sqrt 1-x^2)
13. E (arccos (cosx)=x)
14. D (10.6 mins)

Answer 3

honors student is right but 13 is actually D. (arc cos (cosx)=x)

Answer 4

yeah pig benis is right