Question

Paula is writing short, casual notes for how to find the inverse of a function, f. Those notes are shown below. 1. Write the equation. 2. Replace f(x) with y. 3. Switch x and y. 4. Solve the equation for y. a. If the result does not define y as a function of x, then f has an inverse. b. If the result defines y as a function of x, then f does not have an inverse. 5. Change y to f^−1(x) if f has an inverse. Are Paula's notes correct? If not, identify Paula's error. (1 point) Paula's notes are incorrect. Step 2 should be "Replace f(x) with x." Paula's notes are incorrect. Step 4a should be "If the result does not define y as a function of x, then f does not have an inverse," and step 4b should be "If the result defines y as a function of x, then f has an inverse." Paula's notes are correct. Paula's notes are incorrect. Step 4 should be "Solve the equation for x."

Answer 1

(3rd listed choice) Paula's notes are incorrect. Step 4a should be "If the result does not define y as a function of x, then f does not have an inverse," and step 4b should be "If the result defines y as a function of x, then f has an inverse."

Explanation:

If f(y) = x can be solved for a relation for y that is a function, then f(x) has an inverse. It will be the function defined by y.