Option C, [tex]\left(\dfrac{\pi}{4},\dfrac{5\pi}{4}\right)[/tex] is the correct answer such that the function, [tex]f(x)=12sin(x-4\pi)[/tex] where, [tex]x[/tex] is the time in [tex]seconds[/tex] and [tex]f(x)[/tex] is the position of the water wave in [tex]ft[/tex] above and below the normal water level.
inverse of the function
The inverse of the function is the mirror image of the function with respect to the dependent variable.
How to determine the inverse of the function?
From the figure, the interval of water wave above the normal water level is [tex]\left(\dfrac{\pi}{4},\dfrac{5\pi}{4}\right)[/tex].
So, the interval of the mirror image of the function with respect to the dependent variable [tex]x[/tex] is [tex]\left(\dfrac{\pi}{4},\dfrac{5\pi}{4}\right)[/tex].
As a result, Option C is the correct answer.
Learn more about the inverse of the function here- https://brainly.com/question/2541698
#SPJ2
