Find the inverse function of f(x) = 3x + 2.

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

Find the inverse function of f(x) = 3x + 2.

Explanation:
To find the inverse, swap the input and output and solve for the new output. Start with y = 3x + 2. Interchange x and y to get x = 3y + 2. Solve for y: subtract 2 to get x - 2 = 3y, then divide by 3 to obtain y = (x - 2)/3. This y is the inverse function, so f^{-1}(x) = (x - 2)/3. You can verify by composing: f(f^{-1}(x)) = 3*(x - 2)/3 + 2 = x, and f^{-1}(f(x)) = (3x + 2 - 2)/3 = x.

To find the inverse, swap the input and output and solve for the new output. Start with y = 3x + 2. Interchange x and y to get x = 3y + 2. Solve for y: subtract 2 to get x - 2 = 3y, then divide by 3 to obtain y = (x - 2)/3. This y is the inverse function, so f^{-1}(x) = (x - 2)/3. You can verify by composing: f(f^{-1}(x)) = 3*(x - 2)/3 + 2 = x, and f^{-1}(f(x)) = (3x + 2 - 2)/3 = x.

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