Question

fie functiile f,g:R->R,sa se determine fog,gof,fof,gog, daca f(X)=3x-4 si g(X)= -x la patrat +1
Ajutati ma va rog cu rezolvarea!

Answer 1

f,g: IR-> IR
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fog = f(g(x))
gof = g(f(x))
fof = f(f(x))
gog = g(g(x))
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f(x) = 3x-4
g(x) = -x² + 1
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fog = f(g(x)) = f(-x²+1) = 3(-x²+1) -4 = -3x² -1
gof = g(f(x)) = g(3x-4) = -(3x-4)² + 1 = -9x² + 24x - 15
fof  =  f(f(x)) = f(3x-4)  = 3(3x-4) + 4 = 9x - 8
gog=g(g(x)) = g(-x² + 1) = - ( -x²+1)² +1 = -x⁴+2x²