Question

Which function is the inverse of f(x)= arccsc x

Answer 1

Let's begin by identifying key information given to us:

`\begin{gathered} f(x)=arccsc(x)_{} \\ f\mleft(x\mright)=y \\ \Rightarrow y=arccsc(x) \\ We\text{ will proceed to i}nterchange\text{ }the\text{ }variables,\text{ we have:} \\ x=arccsc(y) \\ We\text{ will make ''y'' the subject of the formula, we have:} \\ y=(x)/(arccsc)\Rightarrow y=csc(x) \\ y=csc(x) \\ y=f^(-1)\mleft(x\mright) \\ \Rightarrow f^(-1)(x)=csc(x) \\ \\ \therefore f^(-1)(x)=csc(x) \end{gathered}`