What is the inverse of f(x)=-csc(8/9 x) ?

The inverse of f(x)=-csc(8/9 x) is (9arccsc(-x))/8

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inverse of f(x)=-csc(8/9 x)

inverse

f (x) = - csc (\frac{8}{9} x)

\frac{9 arccsc ( - x )}{8}

Solution steps

Solve for

csc (\frac{8}{9} x), y = - csc (\frac{8}{9} x)

csc (\frac{8}{9} x) = - y

csc (a) = b \Rightarrow a = arccsc (b)

\frac{8}{9} x = arccsc (- y)

Solve for

x, \frac{8}{9} x = arccsc (- y)

\frac{9 arccsc ( - y )}{8}

Substitute

y = x

\frac{9 arccsc ( - x )}{8}

f (x) = x - 42

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

- 6 x - 5

y = \frac{x - 5}{x}

f (x) = x^{2} - 6 x - 7

What is the inverse of f(x)=-csc(8/9 x) ?
The inverse of f(x)=-csc(8/9 x) is (9arccsc(-x))/8