Given-f-x-x-2-5x-a-x-gt-1-3x-2-x-b-x-1-if-f-x-passes-through-at-point-2-4-and-lim-x-1-f-x-exist-find-the-value-of-3a-2b-

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

Given f (x) = {\begin{cases} x^{2} - 5 x + a; x > 1 \\ \frac{3 x + 2}{x - b}; x ⩽ 1 \end{cases}

if f (x) passes through at point

(2, - 4) and \lim_{x \to 1} f (x) exist, find

the value of 3 a + 2 b .

Answered by MM42 last updated on 06/Jul/23

f (2) = - 4 \Rightarrow 4 - 10 + a = - 4 \Rightarrow a = 2

f (1^{+}) = 1 - 5 + 2 = - 2

f (1^{-}) = \frac{5}{1 - b} = - 2 \Rightarrow b = \frac{7}{2}

\Rightarrow 3 a + 2 b = 13 ✓

Commented by horsebrand11 last updated on 07/Jul/23

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