Respuesta :

jcherry99

Answer:

Step-by-step explanation:

y = Cos(2x)

Inverses for trig functions are found the same way as any other inverse. The trick is to interchange x and y.

x = cos(2y)             Take the inverse cos of both sides.

cos-1(x) = 2y           Divide by 2

1/2 cos-1(x) = y

ajeigbeibraheem

The equation for the inverse of the function y = cos 2x. Thus, Option D is correct.

The inverse of a function f(y) refers to a property in which for every value of y in Y, there must be one x in (X) in a way that f(x) = y.

The inverse of a function reverses the effect of the original function.

Given that:

  • y = cos 2x

2y = cos⁻¹ x   provided that (y ∈ ║ -1, +1 ║)

∴

[tex]\mathbf{y = \dfrac{cos ^{-1}x}{2}}[/tex]

[tex]\mathbf{y = \dfrac{1}{2} \ cos ^{-1} \ x}[/tex]

Therefore, we can conclude that the inverse of y = cos 2x is [tex]\mathbf{ \dfrac{1}{2} \ cos ^{-1} \ x}[/tex]. Option D is correct.

Learn more about the inverse of a function here:

https://brainly.com/question/10300045?referrer=searchResults

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