Question

Which sequence gives the standard method to find an inverse of a function?

Options

• Differentiate \(f(x)\), integrate the result, and interchange the variables.

• Interchange \(x\) and \(y\), write \(y=f(x)\), solve for \(x\), then check invertibility.

• Write \(y=f(x)\), replace \(f(x)\) by \(y\) and solve for \(x\) in terms of \(y\), interchange \(x\) and \(y\), and identify \(f^{-1}(x)\).

• Set \(x=0\), solve for \(y\), and use the resulting constant as \(f^{-1}(x)\).

Answer 1

The standard method begins with \(y=f(x)\), followed by solving for \(x\) in terms of \(y\). Interchanging \(x\) and \(y\) gives the expression for \(f^{-1}(x)\), provided the function is invertible.