Your final answer will be: 16x^4 - 80x^3 + 138x^2 - 95x + 24
I will assume that the first equation is:
f(x) = 2x^2 - 5x + 3
and the second equation is:
4x^2 - 12x + 09.
To find f(g(x)) you need to plug in the equation of g(x) as x into the equation of f(x). So you get:
4(2x^2 - 5x + 3)^2 - 5(2x^2 - 5x + 3) + 3.
That then equals to:
4(4x^4 - 20x^3 + 37x^2 - 30x+9) - 5(2x^2 - 5x + 3) + 3.
Further simplified you get:
16x^4 - 80x^3 + 148x^2 - 120x + 36 - 10x^2 + 25x - 15 + 3.
That simplifies to:
16x^4 - 80x^3 + 138x^2 - 95x + 24.
Answer:
[tex](fg)(x)= 16x^4 - 80x^3 + 124x^2 -60x +9[/tex]
Step-by-step explanation:
In general, the composition of fuction is :
(fg)(x) = f(g(x))
In our case, we do the next:
[tex]f(x) = 2x^2-5x+3[/tex]
[tex]g(x) = 4x^2-12x+9[/tex]
and the composition is
[tex]4(2x^2-5x+3)^2-12(2x^2-5x+3)+9[/tex]
The first term is:
[tex]2x^2-5x+3 = (2x^2-5x+3)(2x^2-5x+3) = 4x^4-20x^3+37x^2-30x+9[/tex]
⇒ [tex]4(4x^4-20x^3+37x^2-30x+9)-12(2x^2-5x+3)+9[/tex]
⇒[tex]16x^4-80x^3+148x^2-120x+36-12\left(2x^2-5x+3\right)+9[/tex]
⇒[tex]16x^4-80x^3+148x^2-120x+36-24x^2+60x-36+9[/tex]
Simplifying, we have
⇒[tex]16x^4-80x^3+124x^2-60x+9[/tex]
