Define f(x)={∣x−2∣x−2,x≠20,x=2andg(x)=f(x)x−4.f(x)=\begin{cases}\dfrac{|x-2|}{x-2}, & x\ne2\\[6pt]0, & x=2\end{cases}\quad\text{and}\quad g(x)=\frac{f(x)}{x-4}.…

Mathematics

Problem

Define f(x)={∣x−2∣x−2,x≠20,x=2andg(x)=f(x)x−4.f(x)=\begin{cases}\dfrac{|x-2|}{x-2}, & x\ne2\\[6pt]0, & x=2\end{cases}\quad\text{and}\quad g(x)=\frac{f(x)}{x-4}. Which statement correctly classifies the discontinuities of gg? a) Removable at x=2x=2; vertical asymptote at x=4x=4 b) Jump at x=2x=2; vertical asymptote at x=4x=4 c) Jump at x=2x=2; removable at x=4x=4 d) Vertical asymptotes at both x=2x=2 and x=4x=4

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