What is the inverse of f(x)=18ln(tan(x)) ?

The inverse of f(x)=18ln(tan(x)) is arctan(e^{x/(18)})

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inverse of f(x)=18ln(tan(x))

inverse

f (x) = 18 ln (tan (x))

arctan (e^{\frac{x}{18}})

Solution steps

Solve for

tan (x), y = 18 ln (tan (x))

tan (x) = e^{\frac{y}{18}}

tan (a) = b \Rightarrow a = arctan (b)

arctan (e^{\frac{y}{18}})

Substitute

y = x

arctan (e^{\frac{x}{18}})

f (x) = \frac{x + 1}{3 x + 4}

tan (0.73)

f (x) = \frac{10 + 4 x}{5 x + 6}

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

1 - e^{- \frac{x}{2}}

What is the inverse of f(x)=18ln(tan(x)) ?
The inverse of f(x)=18ln(tan(x)) is arctan(e^{x/(18)})