To find the answer to this question you have to put the equation in terms of '2x + 1' rather than in terms of 'x'. This means that we need to rearrange the equation a bit:
So, f(2x + 1) = 4x² + 4x + 7
= (2x)² + 4x + 7
= (2x + 1)² - (4x + 1) + 4x + 7
{We do this last step because when we change '2x' to become '2x + 1' we have to take into account that if we multiplied out these brackets we would get:
(2x + 1)² = 4x² + 4x + 1 , and since we only originally had '4x²' we have to subtract '4x + 1'}
= (2x + 1)² - 4x + 4x - 1 + 7
= (2x + 1)² + 6
This equation is now in a form we can now deal with.
So now,
f(x) = x² + 6
Hope this isn't too confusing. 