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# HW plz help urgent

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1)What is the domain of the function $$f(x) = \sqrt{3x+6} - 7$$? Answer in interval notation.

2)Express the domain of $$f(x) = \dfrac{\sqrt{-2x+7}}{x}$$ in interval notation.

3)Express the domain of $$f(x) = \dfrac{\sqrt{x+1}}{(x-2)(x-4)}$$ in interval notation.

Sep 14, 2019

#1
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1. the range of x is going to be like a ray, with a end point while goes to infinity in another direction.

$$f(x)=\sqrt{{\color{red}3}x+{\color{red}6}}-7$$

You do $$(-1)*\frac{{\color{red}6}}{{\color{red}3}}\Rightarrow-2$$

This means the minimum of x is -2, while the maximum goes to infinity.

Sep 14, 2019
#2
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2.       √[-2x + 7]

________

x

First of all....note that x CANNOT  =  0   because this would mean that we are dividing by 0 which is undefined

Also....under the radical.....    -2x + 7  must be   ≥ 0

So

-2x + 7  ≥  0

-2x  ≥ - 7       divide both sides by -2   and reverse the inequality sign

x  ≤ 7/2

So....the domain is

(-infinity, 0)  U  ( 0, 7/2)

See the graph here to confirm this :  https://www.desmos.com/calculator/qg90mexgvo

Sep 14, 2019
#3
+103858
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3.      √ [ x + 1]

___________

(x - 2) (x - 4)

First note that   if x = 2   or x = 4......the denominator  = 0....so.....these two values are not in the domain

Also...under the radical.....x + 1  must be  ≥  0

So

x + 1  ≥ 0

x  ≥ -1

So   the domain is

[ -1, 2)  U (2, 4)  U (4, infinity)

See the graph here : https://www.desmos.com/calculator/a4regqy27f

Sep 14, 2019