What is the inverse of f(x)=csc^2(x) ?

The inverse of f(x)=csc^2(x) is arccsc(sqrt(x)),arccsc(-sqrt(x))

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inverse of f(x)=csc^2(x)

inverse

f (x) = csc^{2} (x)

arccsc (x), arccsc (- x)

Solution steps

Solve for

csc (x), y = csc^{2} (x)

csc (x) = y, csc (x) = - y

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

arccsc (y), arccsc (- y)

Substitute

y = x

arccsc (x), arccsc (- x)

\frac{8}{1 - x ^{3}}

f (x) = \frac{2 x + 7}{x - 1}

y = 1 + \frac{2}{x - 1}

x - 9

f (x) = \frac{8 - x}{7 + x}

What is the inverse of f(x)=csc^2(x) ?
The inverse of f(x)=csc^2(x) is arccsc(sqrt(x)),arccsc(-sqrt(x))