What is the inverse of f(x)=5csc((x+pi)/(2.1))-6.5 ?

The inverse of f(x)=5csc((x+pi)/(2.1))-6.5 is 2.1arccsc((x+6.5)/5)-pi

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inverse of f(x)=5csc((x+pi)/(2.1))-6.5

inverse

f (x) = 5 csc (\frac{x + π}{2.1}) - 6.5

2.1 arccsc (\frac{x + 6.5}{5}) - π

Solution steps

Solve for

csc (\frac{x + π}{2.1}), y = 5 csc (\frac{x + π}{2.1}) - 6.5

csc (\frac{x + π}{2.1}) = \frac{y + 6.5}{5}

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

\frac{x + π}{2.1} = arccsc (\frac{y + 6.5}{5})

Solve for

x, \frac{x + π}{2.1} = arccsc (\frac{y + 6.5}{5})

2.1 arccsc (\frac{y + 6.5}{5}) - π

Substitute

y = x

2.1 arccsc (\frac{x + 6.5}{5}) - π

What is the inverse of f(x)=5csc((x+pi)/(2.1))-6.5 ?
The inverse of f(x)=5csc((x+pi)/(2.1))-6.5 is 2.1arccsc((x+6.5)/5)-pi