What is the inverse of f(x)=2csc(((x+pi))/2)-2 ?

The inverse of f(x)=2csc(((x+pi))/2)-2 is 2arccsc((x+2)/2)-pi

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inverse of f(x)=2csc(((x+pi))/2)-2

inverse

f (x) = 2 csc (\frac{( x + π )}{2}) - 2

2 arccsc (\frac{x + 2}{2}) - π

Solution steps

Solve for

csc (\frac{x + π}{2}), y = 2 csc (\frac{x + π}{2}) - 2

csc (\frac{x + π}{2}) = \frac{y + 2}{2}

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

\frac{x + π}{2} = arccsc (\frac{y + 2}{2})

Solve for

x, \frac{x + π}{2} = arccsc (\frac{y + 2}{2})

2 arccsc (\frac{y + 2}{2}) - π

Substitute

y = x

2 arccsc (\frac{x + 2}{2}) - π

f (x) = 4 - 5 x^{2}

y = 3 x^{2} + 6 x + 15

\frac{1 + 2 \cdot z ^{- 2}}{1 + \frac{1}{2 \cdot z ^{- 2}}}

\frac{x - 4}{2 x + 1}

f (x) = - 0.7 x + 35

What is the inverse of f(x)=2csc(((x+pi))/2)-2 ?
The inverse of f(x)=2csc(((x+pi))/2)-2 is 2arccsc((x+2)/2)-pi