Find the inverse function f^(-1)(x) for f(x) = (3x - 5) / 2.
Answer and explanation
Correct answer: C. (2x + 5) / 3
- Step 1: Set y = (3x - 5) / 2 and swap variables to solve for y: x = (3y - 5) / 2.
- Step 2: Multiply by 2: 2x = 3y - 5.
- Step 3: Add 5 and divide by 3: 3y = 2x + 5 => y = (2x + 5) / 3.
Answer
(2x + 5) / 3.
Why not the others: Option (2x - 5) / 3 fails to change the sign of 5 when moving across the equals sign. Option (3x + 5) / 2 swaps coefficients 2 and 3 incorrectly. Option (2x + 3) / 5 exchanges constants erroneously.
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