9000007203

Consider the function $$f(x)=\mathrm{sgn}(x-2)$$ defined on $\mathrm{Dom}(f)={\mathbb{R}}^{-}$. Find the parameters $a$ a $b$ and domain of the linear function $$g(x)=ax+b$$ which ensure that $f$ and $g$ are identical functions. $$$$ Hint: The function $y=\mathrm{sgn}(x)$ is the sign function. The values of sign function is $1$ for each positive $x$, $-1$ for each negative $x$ and $0$ if $x=0$.