Let , which is one-to-one. If is the inverse function of , what is ?
Answer and explanation
Correct answer: C.
- Step 1: Use the inverse function derivative rule: .
- Step 2: Find by solving : . By inspection, is the unique real solution, so .
- Step 3: Differentiate : . Evaluate at : . Thus, .
Answer
.
Why not the others: Other options evaluate directly or invert the function value incorrectly rather than using the inverse derivative formula .
Practise more Differentiation.
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