Question

functii clasa a zecea

Answer 1

Răspuns:

f(x)=(3x-4)/(x-2) studiem injectivitatea

Fie x1,x2  a.i  f(x1)=f(x2)

(3x1-4)/(x1-2)=(3x2-4)/(x2-2)

(3x1-4)(x2-2)=(3x2-4)(x1-2)

3x1x2-4x2-6x1+8=3x2x1-4x1-6x2+8

-4x2-6x1=-4x1-6x2

2x2=2x1=>c1=x2 Deci f(x1)=f(x2)=.x1=x2

Functia injectiva

Surjectiivitate

f(x)=y

y=(3x-4)/(x-2)

yx-2y=3x-4

yx-3x=2y-4

x(y-3)=2y-4

x=(2y-4)/(y-3)

y≠3 deci imf =codomeniul R\{3]=> functia e surjectiva

Daca o functie e injectiva si surjefctiva atunci e bijectiva

2o functie bijecticva e inversabila

Pornim de la relatia   anterioara

x=(2y-4)/(y-3)

....Explicație pas cu pas: