# Thread: A little help sir

1. ## A little help sir

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..

2. Originally Posted by ranthrave
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..
$\displaystyle 1 \leq x \leq 4 \Rightarrow 3 \leq 3x \leq 12 \Rightarrow 8 \leq 5+3x \leq 17$

So the range is the set $\displaystyle \{y: 8 \leq y \leq 17\}$

3. Originally Posted by ranthrave
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..
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

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