Question

Expresia functiei liniare f:R->R, stiind ca f(-x+3)=5x+2, este?

Answer 1

 

$\displaystyle\\f(x)=ax+b\\\\f(-x+3)=a(-x+3)+b=-ax+3a+b\\\\f(-x+3)=5x+2\\\\-ax+3a+b=5x+2\\\\\text{Scriem ecuatiile:}\\\\-a=5\\3a+b=2\\-----\\\boxed{a=-5}\\\\3\cdot(-5)+b=2\\-15+b=2\\b=2+15\\\boxed{b=17}\\\\\implies \boxed{f(x)=-5x+17}\\\\\text{Verificare:}\\\\f(-x+3)=-5(-x+3)+17=5x-15+17=5x+2~~~\text{(Corect)}$