Answer:
The answer if F ⇒ false
Step-by-step explanation:
* Lets explain the problem
- cos^-1(-x) means f(x) = cos^-1(-x)
- -cos^-1(x) means g(x) = -cos^-1(x)
- The domain of the functions is -1 ≤ x ≤ 1
* Now lets find the the range
∵ f(-1) = cos^-1(- -1) = cos^-1(1) = 0
∵ f(1) =cos^-1(-1) = π
* We have range from 0 to π
∴ The range is 0 ≤ f(x) ≤ π
∵ g(-1) = -cos^-1(-1) = -π
∵ g(1) = -cos^-1(1) = 0
∴ The range is -π ≤ g(x) ≤ 0
- f(-1) ≠ g(-1)
- f(1) ≠ g(1)
* The two sides cannot be equal
* Look to the attached graph
- The blue is cos^-1(-x)
- The green is -cos^-1(x)
-The black is cos^-1(x)
* If h(x) = cos^-1(x)
∴ f(x) = cos^-1(-x) is the image of h(x) when reflected about y-axis
∴ g(x) = -cos^-1(x) is the image of h(x) when reflected about x-axis
* The answer if F ⇒ false
