Let f(x) = 3x2 – x + 2 and g(x) = 5x2 – 1. find f(g( show each step of your work. give a very detailed answer only

f(g(x)) means you put g(x) where x is in the definition of f(x). Doing that, we have

... f(g(x)) = f(5x²-1) = 3(5x²-1)² -(5x²-1) +2

From here, it is a matter of simplifying.

... = 3(25x⁴ -10x² +1) -5x² +1 +2 . . . . . multiply out the square: (a+b)² = a²+2ab+b²

... = 75x⁴-30x² -5x² +3 +1 +2 . . . . . . . eliminate parentheses. Collect terms next.

... f(g(x)) = 75x⁴ -35x² +6