Question

cho f(x)=ax+b.Biết f(0)=0, cmr: f(x)=-f(-x)

M.n giải giùm mk nhanh vs, cần gấp

Answer 1

Vì \(f\left(0\right)=0\) nên :

\(a.0+b=0\)

\(\Rightarrow b=0\)

\(\Rightarrow\left\{{}\begin{matrix}f\left(x\right)=ax\\-f\left(-x\right)=-\left(-ax\right)=ax\end{matrix}\right.\)

\(\Rightarrow f\left(x\right)=-f\left(-x\right)\)

Answer 2

f(0)=0

=>0.a+b=0<=>b=0

=>f(x)=ax

Ta có:

f(x)=ax

-f(-x)=-[a.(-x)]=-(-ax)=ax

=>f(x)=-f(-x)(ĐPCM)