### Home > PC > Chapter 3 > Lesson 3.3.1 > Problem3-113

3-113.

Given $f ( x ) = \left\{ \begin{array} { l l } { a x ^ { 2 } + b \:\text { for } } & \:\:\:{ x < 0 } \\ { 2 a x + 5\: \text { for } } & { 0 \leq x < 1 } \\ { 3 x - b } \:\:\:\:\text { for } & \:\:\:{x \geq 1 } \end{array} \right.$, find the values of $a$ and $b$ so that $f\left(x\right)$ is continuous  at both $x = 0$ and $x = 1$

$ax^2+b=2ax+5\text{ for }x=0$

$2ax+5=3x-b\text{ for }x=1$

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