Select the best answer from the choices provided.
cos^-1(-x)=-cos^-1x for -1≤x≤1.

true of false.

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