Answer:
<em>Correct answer:</em>
<em>A. I and II</em>
<em></em>
Step-by-step explanation:
First of all, let us have a look at the steps of finding inverse of a function.
1. Replace y with x and x with y.
2. Solve for y.
3. Replace y with 
Given that:
Now, let us find inverse of each option one by one.
I. y = x, a(x) = x
Replacing y with and x with y:
x = y
x = 
= 
Hence, I is true.
II. 
Replacing y with and x with y:
= Hence, II is true.
III. 
Replacing y with and x with y:
Hence, III is not true.
IV. 
Replacing y with and x with y:
![x =y^{3}\\\Rightarrow y = \sqrt[3] x\\\Rightarrow a^{-1}(x) = \sqrt[3]{x} \ne a(x)](https://tex.z-dn.net/?f=x%20%3Dy%5E%7B3%7D%5C%5C%5CRightarrow%20y%20%3D%20%5Csqrt%5B3%5D%20x%5C%5C%5CRightarrow%20a%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%7D%20%5Cne%20a%28x%29)
Hence, IV is not true.
<em>Correct answer:</em>
<em>A. I and II</em>
<em></em>
Answer: There are two solutions and they are
theta = 135
theta = 225
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Explanation:
Recall that x = cos(theta). Since the given cosine value is negative, this indicates x < 0. Theta is somewhere to the left of the y axis, placing it in quadrant 2 or quadrant 3.
It turns out there are two solutions, with one solution per quadrant mentioned above. Use the unit circle to find that the two solutions are:
theta = 135
theta = 225
You're looking for points on the unit circle that have x coordinate equal to x = -sqrt(2)/2. Those two points correspond to the angles of 135 and 225, which are in quadrants 2 and 3 respectively.
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I recommend using your calculator to note that
-sqrt(2)/2 = -0.70710678
cos(135) = -0.70710678
cos(225) = -0.70710678
The decimal values are approximate. Make sure your calculator is in degree mode. Because those three results are the same decimal approximation, this indicates that cos(135) = cos(225) = -sqrt(2)/2.
1. The value of x is 4. X + 4 = 4 + 4 = 8
