Funcion Inversa

Dado:
f(x)=3x-4
g(x)=2x^2+1
h(x)=x^2+2x-3
j(x)=3x^2-5
k(x)=x^3-2
l(x)=1/(x-3)
m(x)=1/(x^2+1)

Hallar:
(f+g)(x)=(3x-4)+(2x^2+1)
(f+g)(x)=3x-4+2x^2+1
(f+g)(x)=2x^2+3x-3(f-g)=(3x-4)-(2x^2+1)
(f-g)=3x-4-2x^2-1
(f-g)=-2x^2+3x-5


(f+h+j)(x)=(3x-4)+(x^2+2x-3)+(3x^2-5)
(f+h+j)(x)=3x-4+x^2+2x-3+3x^2-5
(f+h+j)(x)=4x^2+5x-12(h+j-k)(x)=(x^2+2x-3)+(3x^2-5)-(x^3-2)
(h+j-k)(x)=x^2+2x-3+3x^2-5-x^3-5-x^3+2
(h+j-k)(x)=-x^3+4x^2+2x-6


(f-h)+(j-k)=[(3x-4)-(x^2+2x-3) ]+[(3x^2-5)-(x^3-2)]
(f-h)+(j-k)=(3x-4-x^2-2x+3)+(3x^2-5-x^3+2)(f-h)+(j-k)=-x^2+x-1+3x^2-x^3-3
(f-h)+(j-k)=-x^3+2x^2+x-4




(fog)(x)=f[g(x) ]=f(2x^2+1)
(fog)(x)=3(2x^2+1)-4
(fog)(x)=6x^2+3-4
(fog)(x)=6x^2-1


(gof)(x)=g[f(x) ]
(gof)(x)=g(3x-4)(gof)(x)=2(3x-4)^2+1
(gof)(x)=2(9x^2-24x+16)+1
(gof)(x)=18x^2-48x+32+1
(gof)(x)=18x^2-48x+33


(goh)(x)=g[h(x)]
(goh)(x)=g(x^2+2x-3)
(goh)(x)=2(x^2+2x-3)^2+1
(goh)(x)=2(x^4+4x^3-2x^2-12x+9)+1(goh)(x)=2x^4+8x^3-4x^2-24x+18+1
(goh)(x)=2x^4+8x^3-4x^2-24x+19


(jok)(x)=j[k(x)]
(jok)(x)=j(x^3-2)
(jok)(x)=3(x^3-2)^2-5
(jok)(x)=3(x^6-4x^3+4)-5
(jok)(x)=3x^6-12x^3+12-5
(jok)(x)=3x^6-12x^3+7(loh)(x)=l[h(x) ]
(loh)(x)=l(x^2+2x-3)
(loh)(x)=1/((x^2+2x-3)-3)
(loh)(x)=1/(x^2+2x-3-3)
(loh)(x)=1/(x^2+2x-6)




(moj)(x)=m[j(x)]
(moj)(x)=m(3x^2-5)
(moj)(x)=1/((3x^2-5)^2+1)(moj)(x)=1/(9x^4-30x^2+25+1)
(moj)(x)=1/(9x^4-30x^2+26)


(jom)(x)=j[m(x) ]
(jom)(x)=j(1/(x^2+1))
(jom)(x)=3(1/(x^2+1) )^2-5
(jom)(x)=3(1/(x^4+2x^2+1))-5
(jom)(x)=3/(x^4+2x^2+1)-5(jom)(x)=(3-5(x^4+2x^2+1))/(x^4+2x^2+1)
(jom)(x)=(3-5x^4-10x^2-5)/(x^4+2x^2+1)
(jom)(x)=(-5x^4-10x^2-2)/(x^4+2x^2+1)











Defina:

Función inyectiva:

Una función es inyectiva si a cada valordel conjunto (dominio) le corresponde un valor distinto en el conjunto (imagen) de . Es decir, a cada elemento del conjunto A le corresponde un solo valor de B tal que, en el conjunto A no puede...