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Write in Interval form/notation

Write in Interval form/notation-example-1

1 Answer

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Answer: (-∞, -1] and (0, 2)

Explanation:

Can't compare f(x) = x+1 when x<=0 with g(x)=x+1 when x>-1 since the functions are equal between -1<x<=0.

Compare f(x) = 3 when x>0 with g(x)=x+1 when x>-1

g(x) can't be greater than or equal to f(x):

g(x)<f(x)

x+1<3

x+1-1<3-1

x<2 and x>0 ==> 0<x<2

0<x<2 ==> (0, 2) ==> x is between 0 and 2 not including 0 and 2.

Compare f(x) = x+1 when x<=0 with g(x)=2x when x<=-1. Both equations have common x-values at x<=-1.

g(x)<f(x)

2x<x+1

2x-x<x-x+1

x<1 and x<=-1 ==> x<=-1

x<=-1 ==> (-∞, -1] ==> x is between -∞ and -1 not including -∞ but including -1.

(-∞, -1] and (0, 2)

User Tim Dorr
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