Question

determine a função afim f(x)=ax+b, sabendo que f(1)=5 e f(-3)=-7

Answer 1

f(x)=ax+b

f(1)=5 f(1)=a.1+b 1a+b=5

f(-3)=-7 f(-3)=-a.3+b 3a+b=-7


$\left \{ {{a+b=5} \atop {-3a+b=-7}}$

se a+b=5, a=5-b

-3(5-b)+b=-7
-15+3b+b=-7
-15+4b=-7
4b=15-7
4b=8
b=8tex] \frac{8}{4}[/tex]
b=2

a+b=5
a+2=5
a=5-2
a=3

Answer 2

f(x) = ax + b
f(1)=5⇒1·a+b=5⇒a+b=5
f(-3)=-7 ⇒ (-3)·a+b=-7 ⇒ 3a-b=7
(a+b) + (3a -b) = 5 + 7 ⇒ 4a = 12 ⇒ a = 3
a + b = 5 ⇒ 3 + b = 5 ⇒b = 2
logo f(x) = 3x + 2