Let f(x) = 2 Domain: x less than or equal to -1
= ax+b Domain: -1 less than x or less than 3
= -2 Domain: x greater or equal to 3
Find a and b such that f is continuous.
Hello, Nimmy,Originally Posted by Nimmy
I've attached a diagram to show you what you have to calculate:
In short: There are 2 points which are connected by a straight line. So you know 2 points of this line. Use the 2-point-formula of a line to get the equation.
(You should get f(x)=-x+1, -1 < x < 3)
It it is certainly countinous because there are constant and linear function where are always countinous.Originally Posted by Nimmy
However we need to check
Let us do -1 first,
By definition of countinuity we need that,
But the limit from the left is same as,
And the limit from the right is same as,
Similarly, if we do this for we have,
From these two equations we have,