Question

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

Answer 1

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

Answer 2

$f(g(x))= 3(5x^2 -1)^2 - (5x^2 - 1) + 2\\ f(g(x))= 3(25x^4-10x^2+1)-5x^2+1+2\\ f(g(x))= 75x^4-30x^2+3-5x^2+3\\ f(g(x))=75x^4-35x^2+6$