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

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