Write the equation for the inverse of the function.

y = cos 2x

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:

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

∴

Therefore, we can conclude that the inverse of y = cos 2x is . Option D is correct.

Learn more about the inverse of a function here:

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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

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)