Question

Se considera functiile f:R-R,f(x)=2 x-3 si g :R-R,g(x),g(x)=f(x+3).a)Determinati legea de corespondenta a functiei g. b)Reprezentati grafic cele doua functii in acelasi sistem de axe de coordonate.c)Calculati suma S =f(-1)+f(-2)+....+f(-25)+g(1)+g(2)+....g(26).​

Answer 1

Răspuns:

f(x)=2x-3

g(x)=f(x+3)=2(x+3)-3=

2x+6-3=2x+3

B)f(x)=2x-3

Intersectia cu Ox f(x)=0

2x-3=0

2x=3 x=3/2

A(3/2,0)

Intersecyia cuOy

f(0)=2*0-3=0-3= -3

B(0,-3)

Trasezi dreapta AB

g(x)=2x+3

Intersectia  cu Ox

2x+3=0 2x= -3    x= -3/2     C(-3/2,0)

Intersectia cu Oy

g(0)=2*0+3=3

D(0,3)

Trasezi dreapta CD

c)f(-1)=2*(-1)-3= -2-3= -5

f(-2)=2*(-2)-3= -4-3= -7

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f(-25)=2(-25)-3= -50-3= -53

g(1)=2*1+3= 5

g(2)=2*2+3=7

----------------------

g(25)=2*25+3=53

g(26)=2*26+3=52+3=55

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f(-1)+f(-2)+...+f(-25)+g(1)+g(2)+...+g(25)+g(26)=

-5-7-...-53+5+7+...+53+55= reduci termenii opusi=55

Asteapta atasamentul

Intersectia cu

Explicație pas cu pas: