What is the inverse of f(x)=4arccot((3x)/4-2/3) ?

The inverse of f(x)=4arccot((3x)/4-2/3) is (12cot(x/4)+8)/9

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inverse of f(x)=4arccot((3x)/4-2/3)

inverse

f (x) = 4 arccot (\frac{3 x}{4} - \frac{2}{3})

\frac{12 cot ( \frac{x}{4} ) + 8}{9}

Solution steps

Solve for

arccot (\frac{3 x}{4} - \frac{2}{3}), y = 4 arccot (\frac{3 x}{4} - \frac{2}{3})

arccot (\frac{3 x}{4} - \frac{2}{3}) = \frac{y}{4}

arccot (a) = b \Rightarrow a = cot (b)

\frac{3 x}{4} - \frac{2}{3} = cot (\frac{y}{4})

Solve for

x, \frac{3 x}{4} - \frac{2}{3} = cot (\frac{y}{4})

\frac{12 cot ( \frac{y}{4} ) + 8}{9}

Substitute

y = x

\frac{12 cot ( \frac{x}{4} ) + 8}{9}

- sin (x)

f (x) = 2 tan (4 x)

f (x) = \frac{( 3 x ^{3} - 3 x )}{( x - 1 )}

3 x - 2 y = 12

f (x) = x - 9

What is the inverse of f(x)=4arccot((3x)/4-2/3) ?
The inverse of f(x)=4arccot((3x)/4-2/3) is (12cot(x/4)+8)/9