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

 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

answer: 140

step-by-step explanation:

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