Question

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

Answer 1

I have a solution here to the same problem but a slight different given:

-1 x<=-1 
ax-b -1<x<1 
2 x>=1 

The solution is as follows:

 f(x) = {-1, x ≤ -1 
...... { ax - b, -1 < x < 1 
...... { 2, x ≥ 1 


Then we must have: 
lim(x-->-1) -1 = lim(x-->-1) ax - b 
==> -1 = -a - b 
==> a + b = 1 

And we must have: 
lim(x-->1) ax - b = lim(x-->1) 2 
==> a - b = 2 

So we need to solve the system of equations given by: 
a + b = 1 
a - b = 2 

After doing so, you should get that: 
a = 3/2 
b = -1/2 

By studying the solution above, you now have the ability to answer the problem on your own!