Question

sa se calculeze: (fog) (x) (fof) (x) si (gof) (x) daca f, g:R -> R, f(x) = 2x^2 - x + 3, g(x) = 3x - 2

Answer 1

Răspuns:

Explicație pas cu pas:

f(x)=2x²-x+3

g(x)=3x-2

fog (x)= f(g(x))= f(3x-2)= 2(3x-2)²-(3x-2)+3=18x²-24x+8-3x+5=18x²-27x+13

fof(x)=f(f(x))=f(2x²-x+3)=2(2x²-x+3)²-(2x²-x+3)+3=

fof(x)=8x⁴+2x²+18-4x³+12x²-6x-2x²+x=8x⁴-4x³+12x²-5x+18

gof(x)=g(f(x))=g(2x²-x+3)=3(2x²-x+3)-2=6x²-3x+7