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22 September, 23:14

If f (3x-5) = 6x+7, then find the value of f^2 (x).

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  1. 22 September, 23:38
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    Answer: 4x² + 68x + 289

    Step-by-step explanation:

    f (3x - 5) = 6x + 7

    How can we change 3x into 6x? by multiplying by 2

    Consider that f (x) = 2x, then f (3x - 5) = 2 (3x - 5)

    = 6x - 10

    We are close, but not quite there. How can we change - 10 into + 7? by adding 17

    Now, consider that f (x) = 2x + 17, then f (3x - 5) = 2 (3x - 5) + 17

    = 6x - 10 + 17

    = 6x + 7

    Bingo! So, f (x) = 2x + 17

    Now, let's find f² (x) - -> (2x + 17) ²

    = (2x + 17) (2x + 17)

    = 4x² + 68x + 289
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