Question

20 DE PUNCTE! f(x)=1-2x, g(x)=3x. Sa se calculeze fog,gof,fof,gog

Answer 1

Răspuns:

Explicație pas cu pas:

f,g: IR-> IR

_________________

fog = f(g(x))

gof = g(f(x))

fof = f(f(x))

gog = g(g(x))

_________________

f(x) = 1 - 2x

g(x) = 3x + 1

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fog = f(g(x)) = f(3x+1) = 2(3x+1) -2x = -4x -1

gof = g(f(x)) = g(3x-2x) = -(3x-2) + 1 = -2x + 24x -= 22

fof  =  f(f(x)) = f(3x-2x)  = 3(3x-2x) + 4 = 9x - 8

gog=g(g(x)) = g(-x + 1) = - ( -x+1) +1 = -x+2x = 2

Answer 2

$\it f\circ g =f(g(x))=f(3x)=1-2\cdot3x=1-6x\\ \\ g\circ f=g(f(x))=g(1-2x)=3\cdot(1-2x)=3-6x\\ \\ f\circ f=f(f(x))=f(1-2x)=1-2\cdot(1-2x)=1-2+4x=4x-1\\ \\ g\circ g=g(g(x))=g(3x)=3\cdot3x=9x$