Given f(x) = 3x + 2, what is f^{-1}(10)?

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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

Given f(x) = 3x + 2, what is f^{-1}(10)?

Explanation:
To find f^{-1}(10), think of the inverse as the input that produces 10 when f is applied. Start with y = f(x) = 3x + 2 and solve for x in terms of y: y = 3x + 2 implies x = (y - 2)/3. So f^{-1}(y) = (y - 2)/3, and f^{-1}(10) = (10 - 2)/3 = 8/3. You can check by plugging back: f(8/3) = 3*(8/3) + 2 = 8 + 2 = 10. The value is 8/3.

To find f^{-1}(10), think of the inverse as the input that produces 10 when f is applied. Start with y = f(x) = 3x + 2 and solve for x in terms of y: y = 3x + 2 implies x = (y - 2)/3. So f^{-1}(y) = (y - 2)/3, and f^{-1}(10) = (10 - 2)/3 = 8/3. You can check by plugging back: f(8/3) = 3*(8/3) + 2 = 8 + 2 = 10. The value is 8/3.

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