Question 10 Unsaved Find Numbers a and B or K So That F is Continuous at Every Point
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Question 1 2 pts Find numbers a and b, or k; so that f is continuous at every point: x, X<- ax + b; -4sx <-3 Ix+12 X>-3 f(x) a = 7,b = -12 Impossible a =-7, b =-12 a =-7,b = 12
Related Question
Find numbers a and b so that f(x) is continuous at every point, x X<- f(x) ax+b -2 sx<4 X+12 x>4 A. a =-2,b = 8 B. a = 2,b =-8 C.a =2,b = 8 D: Impossible
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Video Transcript
in this problem we have given a function affects equal X squared When X less than -2. A X plus B. When X is greater than equal -2 and less than equal for an X plus 12. This is X greater than four. So here it is given that fx is continuous for every at every point. So we have to find the value of am Mhm Who Since affects its continuous at every point? So it is also continuous at -2 and four. That is the point given in this function. Who to release use here. The definition of continuity function effects is said to be continuous at any point. A If the limit value of extend to a effects equal to F A. This is the japanese enough continuity. Now we will take here at point X equals -2. This is the point and it's too. So here limit extend to minus two. Fx should be equal to f of minus two because if X is continuous at every point and if X is continuous at X equals minus two. Also taking limit, this is the function where we will we will we will take limit the limit extend to minus two, X Square equals F -2. That is a -2 Plus B. Because here X equal to at the security we have function A X plus B. This is a minus two plus a beat. And this limit will be minus two where minus to a plus b. So here we have minus to a plus b four. Let's take it as a question one. Similarly we will take all these four add X. Equal for The function is continuous. Also limit extend to four effects equal effort. So here again, Equality sign is here. So the functional value four will be calculated by this function and the limit will be calculated by this function. This limit X. 10-4 X plus 12. And here effort, that is A four plus B. So this is four plus 10, that is 16. And for A plus B This equation is four, a plus b equals 16. So let's take it as a question too. Now we will solve the question 1st and 2nd for the value of A and B. So solving here we will have For a plus b equals 16 subjecting this, we will have minus minus and minus here, This is -60 and being minus. Berg will cancel out. And here we have -20. So this will give us two equal true, I'm putting equal to here. We will have four into to just be equal 16. So this is we have year eight plus B Equal 16 We have here being equal eight. The get here the value of A and B equal to and be equal it. This is the answer and in the question it is given in the absence. See so the option C. Is correct. These thank you
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