Sa se determine functia de gradul 1 f:R - R stiind ca:

a) f(1)=2 si f(-2)=7

b) f(2/5)=0 si f(0)=2

c) A(0,3) ∈ Gf si B(1,7) ∈ Gf

d) A(2,4) ∈ Gf si B(6,12) ∈ Gf


Răspuns :

Răspuns:

Explicație pas cu pas:

Vezi imaginea Laura

Răspuns:

f(x)=ax+b

f(1)=a+b=2

f(-2)=-2a=7

a=-7/2

-7/2+b=2

-7+2b=4

2b=4+7

2b=11

b=11/2

f(x)=-7/2x+11/2

b. f(x)=ax+b

f(2/5)=0 si f(0)=2

f(2/5)=2/5a+b=0

f(0)=b=2

2/5a+2=0

2a+10=0

2a=-10

a=-10:2

a=-5

f(x)=-5x+2

c.

A(0,3) ∈ Gf si B(1,7) ∈ Gf

f(0)=3

f(1)=7

f(x)=ax+b

f(0)=b=3

f(1)=a+b=7

a+3=7

a=7-3=4

f(x)=4x+3

d.

A(2,4) ∈ Gf si B(6,12) ∈ Gf

f(2)=4

f(6)=12

f(x)=ax+b

f(2)=2a+b=4

b=4-2a

f(6)=6a+b=12

6a+4-2a=12

4a+4=12 /:4

a+1=3

a=3-1=2

b=4-2a

b=4-2×2=4-4=0

f(x)=2x