Find the inverse function of F(x) = 2 arccosx
F-1(x)=
To find the inverse function of F(x) = 2 arccos(x), we can follow these steps:
Step 1: Replace F(x) with y.
y = 2 arccos(x)
Step 2: Swap x and y.
x = 2 arccos(y)
Step 3: Solve for y.
x/2 = arccos(y)
Step 4: Take the cosine of both sides.
cos(x/2) = y
Step 5: Replace y with F^(-1)(x).
F^(-1)(x) = cos(x/2)
Therefore, the inverse function of F(x) = 2 arccos(x) is F^(-1)(x) = cos(x/2).