If f(x) = (2x + 5) / (x - 3) for x != 3, what is the inverse function f^(-1)(x)?
Answer and explanation
Correct answer: A. f^(-1)(x) = (3x + 5) / (x - 2) for x != 2
- Step 1: Set y = (2x + 5)/(x - 3) and swap variables: x = (2y + 5)/(y - 3). Step 2. Multiply by (y - 3): xy - 3x = 2y + 5. Step 3. Group terms in y: y(x - 2) = 3x + 5. Step 4. Solve for y: y = (3x + 5)/(x - 2). Answer: f^(-1)(x) = (3x + 5) / (x - 2) for x != 2. Why not the others: Reciprocal (x-3)/(2x+5) is 1/f(x), not f^(-1)(x).
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