What inequality is equivalent to |x-4| <8?

1 answer:

Furkat [3]3 years ago

5 0

Answer:

x<《-4,12》

Step-by-step explanation:

inequalities:

x-4<8, x-4>0

-(x-4)<8, x-4-<0

intersections:

x<12, x>4

x>-4, x<4

x<[4,12》

x<《-4,4》

x<《-4,12》

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Sveta_85 [38]

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I think your functions are $y=2^{x}$ , $y=2*5^{x}$ and $y=2+5^{x}$

If yes then then the third function which is $y=2+5^{x}$ .

Step-by-step explanation:

The function $c^{x}$ where c is a constant has

Domain : $c\geq 0$

Range : ( 0 , ∞ )

The above range is irrespective of the value of c.

I have attached the graph of each of the function, you can look at it for visualization.

$y=2*5^{x}$ ⇒ If we double each value of the function $y=5^{x}$ , which has range ( 0 , ∞ ), but still the value of extremes won't change as 0*2=0 and ∞*2=∞. Therefore the range remains as ( 0 , ∞ ).

$y=2+5^{x}$ ⇒ If we add 2 to each value of the function $y=5^{x}$ , which has range ( 0 , ∞ ), the lower limit will change as 0+2=2 but the upper limit will be same as ∞. Therefore the range will become as ( 2 , ∞ ).