Find the inverse function f^(-1)(x) for the one-to-one function f(x) = (3x - 4) / 5.
Answer and explanation
Correct answer: D. (5x + 4) / 3
- Step 1: Set y = f(x): y = (3x - 4) / 5.
- Step 2: Swap x and y: x = (3y - 4) / 5.
- Step 3: Multiply by 5: 5x = 3y - 4.
- Step 4: Add 4: 5x + 4 = 3y.
- Step 5: Divide by 3: y = (5x + 4) / 3.
Answer
(5x + 4) / 3.
Why not the others: '(5x - 4) / 3' makes a sign error when transposing -4; '(3x + 5) / 4' swaps coefficients incorrectly; '5 / (3x - 4)' takes the reciprocal 1/f(x).
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