Question

Find the inverse function:
y=-2cos(3x)

Answer 1

The inverse as in it's negative not it's opposite

Answer 2

the inverse is its reflection over y=x

Answer 3

replace x in the initial equation, with y, and thats your inverse!

Answer 4

I got that far then do I divide the 3 or divide the -2 first? @Rizags

Answer 5

divide by -2

Answer 6

tell me what you get after didividing by -2

Answer 7

x/-2=cos3y

Answer 8

now, take the INVERSE cos of each side. Do you know what that is?

Answer 9

Nope

Answer 10

well, the INVERSE cos essentially undoes the cosine. after taking the inverse cos, you get \[\cos^{-1} (\frac{ -x }{ 2 })=3y\]

Answer 11

then divide both sides by three

Answer 12

tell me when you've done that

Answer 13

x/-2/3?cos^-1=y

Answer 14

@Rizags

Answer 15

lemme write it out

Answer 16

\[y = ±(\frac{1}{3} \cos^{-1}(\frac {-x}{2})\]

Answer 17

thats it

Answer 18

If I'm solving for cosx to find the domain, how would I go about doing that? @Rizags

Answer 19

the domain is all reals

Answer 20

your inverse function is
$$
\Large y = \frac{1}{3} \cos^{-1}(\frac {-x}{2})

$$
the domain of y = arcos (x) is [-1,1]

so the domain of arcos(-x/2) is
-1 <= -x/2 <= 1

Answer 21

that gives you -2 <= x <= 2 for your domain