Question

Determinati a,b apartin R daca functia f:R cu valori in R,f(x)=ax+b verifica conditiile f(1)=1 si f(-3)=-7

Answer 1

f(1)=a+b
f(1)=1

a+b=1

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

-3a+b=-7

a+b=1⇒a=1-b
-3a+b=-7
-3(1-b)+b=-7
-3+3b+b=-7
4b=-7+3
4b=-4
b=-4:4
b=-1

a=1-b
a=1-(-1)
a=1+1
a=2

Answer 2

[tex]f(1)=1\Leftrightarrow a+b=1\\ f(-3)=-7\Leftrightarrow -3a+b=-7[/tex]

$\left \{ {{a+b=1} \atop {-3a+b=-7}} \right. \Leftrightarrow \left \{ {{b=1-a} \atop {-3a+1-a=-7}} \right. \Leftrightarrow \left \{ {{b=1-a} \atop {-4a=-8}} \right. \Leftrightarrow \left \{ {{b=-1} \atop {a=2}} \right.$

$f(x)=ax+b=2x-1$