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

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4 votes

Answer: 4x² + 68x + 289

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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