The intermediate value theorem states the following: Consider an interval I=[a,b] in the real numbers R and a continuous function f:I->R. Then, If u is a number between f(a) and f(b), f(a)<u<f(b) (or f(a)>u>f(b) ), then there is a c∈(a,b) such that f(c)=u.

Jared Lowe 2022-11-20 Answered
The intermediate value theorem states the following: Consider an interval I = [ a , b ] in the real numbers and a continuous function f : I . Then, If u is a number between f ( a ) and f ( b ), f ( a ) < u < f ( b ) (or f ( a ) > u > f ( b ) ),

then there is a c ( a , b ) such that f ( c ) = u.
What happens if we consider R instead of I ?
Is there a simple method to prove the theorem in this case ? I know the method for f : I R with I = [ a , b ], but here it is different.
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Answers (1)

hitturn35
Answered 2022-11-21 Author has 20 answers
The general equation for the point-slope form of a linear equation is y - y 1 = m ( x - x 1 ) , where m is the slope, and ( x 1 , y 1 ) is the known point.
y - ( - 5 ) = - 5 ( x - ( - 3 ) ) =
y + 5 = - 5 ( x + 3 )
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