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Question Number 194429 by horsebrand11 last updated on 06/Jul/23

$$\mathrm{Given}\mathrm{f}\left(\mathrm{x}\right)=\{\begin{array}{l}{\mathrm{x}}^2-5\mathrm{x}+\mathrm{a};\mathrm{x}>1\\ \frac{3\mathrm{x}+2}{\mathrm{x}-\mathrm{b}};\mathrm{x}⩽1\end{array}$$$$\mathrm{if}\mathrm{f}\left(\mathrm{x}\right)\mathrm{passes}\mathrm{through}\mathrm{at}\mathrm{point}$$$$(2,-4)\mathrm{and}\underset{x\to 1}{\lim }\mathrm{f}\left(\mathrm{x}\right)\mathrm{exist},\mathrm{find}$$$$\mathrm{the}\mathrm{value}\mathrm{of}3\mathrm{a}+2\mathrm{b}.$$

Answered by MM42 last updated on 06/Jul/23

$$f\left(2\right)=-4\Rightarrow 4-10+a=-4\Rightarrow a=2$$$$f\left(1^{+}\right)=1-5+2=-2$$$$f\left(1^{-}\right)=\frac{5}{1-b}=-2\Rightarrow b=\frac{7}{2}$$$$\Rightarrow 3a+2b=13✓$$

Commented by horsebrand11 last updated on 07/Jul/23

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