What is the inverse of f(x)=arccos((5x)/(x+12)) ?

The inverse of f(x)=arccos((5x)/(x+12)) is (12cos(x))/(5-cos(x))

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inverse of f(x)=arccos((5x)/(x+12))

inverse

f (x) = arccos (\frac{5 x}{x + 12})

\frac{12 cos ( x )}{5 - cos ( x )}

Solution steps

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

\frac{5 x}{x + 12} = cos (y)

Solve for

x, \frac{5 x}{x + 12} = cos (y)

\frac{12 cos ( y )}{5 - cos ( y )}

Substitute

y = x

\frac{12 cos ( x )}{5 - cos ( x )}

f (x) = \frac{- x - 1}{2 x - 1}

1 - 2 2 x - 5

f (x) = sin (θ)

f (x) = f (x) = x^{3} - 5

What is the inverse of f(x)=arccos((5x)/(x+12)) ?
The inverse of f(x)=arccos((5x)/(x+12)) is (12cos(x))/(5-cos(x))