Question

determine the value b and c that g is continuous. . .

Answer 1

hold on. my computer is being a spaz

Answer 2

\[g(x)=\left\{ x+1;1<x <3 \right\}\]

Answer 3

\[x^2+bc+c; \left| x-2 \right|>1\]

Answer 4

Never, by the way you define your function, it's undefined (hence discontinuous) at x=1 and x=3.

Answer 5

then i must have typed it wrong cause the answer is b=-3, c=4

Answer 6

Yes, you did. There must at least 2 'equal' signs somewhere in the definition of your function.

Answer 7

no. i typed it right. . . . well, according to the wkst.

Answer 8

well if this is the case then the answer is wrong unless you redefine your function so that it's define at x=1and x=3

Answer 9

can you do that?

Answer 10

Yes

Answer 11

ok. how do i go about doing that?

Answer 12

The only problematic points we need to consider are 1 and 3. Take the left-sided limit and right-sided limit at each point, equal them and solve for b,c. Remember to redefine the function at these points after that too or else your whole work means nothing.

Answer 13

I seriously doubt that your function may look like this and you've typed it wrong
\[g(x) = \left\{ {\begin{array}{*{20}{c}}
{x + 1} & {1 < x < 3} \\
{{x^2} + bx + c} & {|x - 2| \ge 1} \\
\end{array}} \right.\]

Answer 14

hold on

Answer 15

here's a pic.

Answer 16

Something must be wrong here. You'd better check with your instructor. Normally in a piecewise-defined function the union of all intervals will form the domain of g, which is not true in this case. (You can see in Q3, the function is defined properly.)

Answer 17

so like for question three, you set 5-x=2x-3

Answer 18

Nope, you take the limits from the left and right, and equal them.

Answer 19

Okay, I gotta go now, so let me write it down anyway. Definition of continuity gives us \[\mathop {\lim }\limits_{x \to a} g(x) = g(a)\], which means both sides need to exist i.e be defined in the domain of g(x). In order for the limit to exist you must check if the right-side limit equals the left-side limit. In order for the value of f(a) to exist you must check if a is in the domain of g(x). That's it! You should form a system of equations after doing all these, which you should be able to solve.

Answer 20

thank you so much for your help!!