Answer:
g(f(x)) =75x² + 90x + 30
Step-by-step explanation:
To find g(fx), all we need to do is to insert f(x) in g(x), that is anywhere x is in g(x), we replace the value of g(x) with x and then simplify
f(x) = 5x + 3 g(x) = 3x² + 3
g(f(x)) = 3(5x + 3)² + 3
Next is to open the parenthesis and then simplify
(5x + 3)² = (5x + 3)(5x + 3) = 5x(5x+3) + 3(5x+3) =25x² +15x +15x+9 = 25x²+30x+9
g(f(x)) = 3(25x² + 30x + 9) + 3
g(f(x)) = 75x² + 90x + 27 + 3
g(f(x)) =75x² + 90x + 30
