Question

Detetmina functia f:|R -> |R f(x) =ax+b daca f(2x -1)=x+4 pentru orice x € |R

Answer 1

f(2x-1)=a(2x-1)+b=x+4
2ax-a+b=x+4
2a=1, a=1/2
-a+b=4
b=4+1/2=9/2
f(x)=x/2+9/2

Answer 2

[tex]\it f(2x-1) = x + 4 \ \ \ (*) [/tex]

$\it Notam\ 2x-1=t \Rightarrow x=\dfrac{t+1}{2}$

[tex]\it Relatia\ (*) \ devine : f(t) = \dfrac{t+1}{2} +4 =\dfrac{t}{2}+\dfrac{1}{2}+4 \Rightarrow \\ \\ \it \Rightarrow f(t) = \it \dfrac{1}{2}t +\dfrac{9}{2}\ \ \ (**)[/tex]

$\it Notam \ t = x\ si\ relatia\ (**) \ devine: \\ \\ f(x) = \dfrac{1}{2}x + \dfrac{9}{2}$