Given f(x) = 2x2 + 4 and g(x) = 3x - 1 What is (fg)(x)? Show work please (:

Answer 1

Hey Mallory,

It's important to look at a small detail for this question. Is this a compound function (f*g)(x), or is it a composite function f(g(x))?

If it's the first compound function then we just multiply the two functions by each other. (2x^2+4)(3x-1). FOIL and you get 6x^2-2x^2+12x-4.

If it's a composite function then f(g(x))= 2(3x-1)^2+4. Square the parentheses we get 2(9x^2-6x+1)+4. Next distribute the 2 to get (18x^2-12x+2)+4, then combine like terms for 18x^2-12x+6.

Hope this helps.

Have a great day and stay safe.

michael.russell.10

Answer 2

f(x)=2x²+4

g(x)=3x-1

(f∘g)(x)=f(g(x))=2(3x-1)²+4=2(9x²-6x+1)+4=18x²-12x+6

Answer 3

(2x^2+4)(3x-1) = 6x^3 -2x^2 + 12x - 4