2. [7/13 Points] PREVIOUS ANSWERS LARCALCET7 3.6.005.MI.SA. ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequential/y. If you skip a part of the question, ynu will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Verify that fhas an inverse function. Then use the function fand the given real number a to nd (f'1)'(a). (Hint: See Example 1. If an answer does not exist, enter DNE.) f(x) = x3 2, a = 123 Step 1 The given function is f(>() = X3 2. Differentiate f(X) with respect to X. XIV /2 f'(x)=3 p3 Step 2 The function f'(x) = 3x2 is always non-negative /) non-negative on the domain of f(x), Therefore, f(x) is g 7,.) is monotonic on the domain of x and the inverse of the function exists. Step 3 To find r100, let y= f(x) and solve for x, y = x3 2 x= (y+2)1/3 /1/3 Interchange x and y in the expression for X. 1/: v / 1/3 y=