Invertible Function Practice

1 : Find the inverse for the function $f(x) = \sage {p1f1}$ .

$f^{-1}(x) = \answer {\sage {p1ans1}}$

Recall; to find an inverse analytically you can switch the input/output variables (replace “ $f(x)$ ” with “ $y$ ” first) and then re-solve for $y$ . Alternatively you can just solve the original expression for $x$ . In order to undo a power, use the associated root, and for the love of God don’t expand any of these polynomials or you will go insane!

2 : Find the inverse for the function $f(x) = \sage {p2f1}$ .

$f^{-1}(x) = \answer {\sage {p2ans1}}$

Recall; to find an inverse analytically you can switch the input/output variables (replace “ $f(x)$ ” with “ $y$ ” first) and then re-solve for $y$ . Alternatively you can just solve the original expression for $x$ . In order to undo a power, use the associated root, and for the love of God don’t expand any of these polynomials or you will go insane!

3 : Find the inverse for the function $f(x) = \sage {p3f1}$ .

$f^{-1}(x) = \answer {\sage {p3ans1}}$

Recall; to find an inverse analytically you can switch the input/output variables (replace “ $f(x)$ ” with “ $y$ ” first) and then re-solve for $y$ . Alternatively you can just solve the original expression for $x$ . In order to undo a power, use the associated root, and for the love of God don’t expand any of these polynomials or you will go insane!