Question

For what values of a and b is the following function is continuous at every x:

-7 x ≤ -3
f(X) = ax-b -3< x < 1
3 x ≥ 1
Find the values is a and b ix f(x) continuous at every x?

Answer 1

Let me try to help.
According to the problem, we have:
f(-3) = -7
f(1) = 3
Therefore,when we replace x with -3,then x with 1 into f(x) = ax-b, we have:
-7 =-3a-b (#1)
3 =a-b (#2)
we can solve this system of equations by the elimination method, for example.
let's multiply both side of the second equation by -1(in order to eliminate the variable b)
we have found a third equation: -3 = -a+b (#3)
Now, by addition of the equations #1 and #3, we've got:
-10 = -4a
or 10 = 4a (by Multiplying both sides by -1)
or a=10/4
or a=5/2
when we replace a = 5/2 into the equation (#3), we've found b=-1/2.
The function can be written then: f(x) =( 5/2)x -(-1/2) or f(x) = (5/2)x + 1/2
I Hope I've help you.

Answer 2

I hope I've helped you.

Answer 3

Yes very much so,