What is the inverse of f(x)= 1/2 arccos(pix)-3 ?

The inverse of f(x)= 1/2 arccos(pix)-3 is (cos(2x+6))/pi

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inverse of f(x)= 1/2 arccos(pix)-3

inverse

f (x) = \frac{1}{2} arccos (π x) - 3

\frac{cos ( 2 x + 6 )}{π}

Solution steps

Solve for

arccos (π x), y = \frac{1}{2} arccos (π x) - 3

arccos (π x) = 2 y + 6

arccos (a) = b \Rightarrow a = cos (b)

π x = cos (2 y + 6)

Solve for

x, π x = cos (2 y + 6)

\frac{cos ( 2 y + 6 )}{π}

Substitute

y = x

\frac{cos ( 2 x + 6 )}{π}

\frac{1}{5} x - 1

f (x) = \frac{80 x}{x + 60}

f (x) = \frac{16}{x - 6}

f (x) = \frac{1}{4} x + 2

ln (4.77)

What is the inverse of f(x)= 1/2 arccos(pix)-3 ?
The inverse of f(x)= 1/2 arccos(pix)-3 is (cos(2x+6))/pi