Q. If the domain of the fxn y=5+3x is the set {x: 1 ≤ x ≤ 4} find the range of the fxn and express it as a set..

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- Jul 16th 2008, 08:09 AM #1

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- Jul 16th 2008, 10:08 AM #2

- Jul 16th 2008, 11:15 AM #3
Alternatively notice that $\displaystyle f(x)$ is increasing $\displaystyle \forall{x}\in\mathbb{R}$

Therefore we should have that $\displaystyle x_0<x_1\Rightarrow{f(x_0)<f(x_1)}$

So the maximum on this interval should be $\displaystyle f(\text{smallest x-value})$ and the largest $\displaystyle f(\text{largest x-value})$

So

$\displaystyle f(1)\leq{y}\leq{f(4)}\Rightarrow{8\leq{y}\leq{17}}$