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Question Number 180485 by moh777 last updated on 12/Nov/22

$$Determinethevalueofaandb,$$$$thatmakethefunctionf\left(x\right)continuity$$$$f\left(x\right)=\{\begin{array}{l}x+3,x\lneqq 4\\ 2ax+b,x=4\\ x^2-3,x\gneqq 4\end{array}$$

Commented by Frix last updated on 12/Nov/22

$$\mathrm{this}\mathrm{is}\mathrm{not}\mathrm{possible},\mathrm{check}\mathrm{the}\mathrm{question}$$$$\underset{x\to 4^{-}}{\lim }f\left(x\right)=7\ne 13=\underset{x\to 4^{+}}{\lim }f\left(x\right)$$$$\mathrm{we}\mathrm{need}\mathrm{a}\mathrm{vertical}\mathrm{line}\mathrm{to}\mathrm{connect}\mathrm{both}\mathrm{but}$$$$\mathrm{a}\mathrm{vertical}\mathrm{line}\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{function}$$$$\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{this}\mathrm{would}\mathrm{be}$$$$x=4,7⩽y⩽13$$

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