Explanation:
(f○g)(x) = f(g(x))
it simply means that we put the expression of g(x) into ask places of x in f(x).
(f○g)(x) = g(x)² + 3
therefore,
g(x)² + 3 = 9x² - 12x + 7
g(x)² = 9x² - 12x + 4 = (a + b)² = a² + 2ab + b²
9x² = a² tells us that a = ±3x
4 = b² tells us that b = ±2
which signs of a and b do we need ?
-12x = 2ab gives us the answer
-6x = ab
that means the signs need to be opposite and we have 2 possible solutions
g(x) = 3x - 2
or
g(x) = -3x + 2