Not sure how do do this. Please help?

Find all values of a and b so that the function is continuous for all x E R.

f(x)= −3a + 4(x^5)b x ≤ −1

{ ax − 2b −1 < x < 1

3x^2 − bx + a x ≥ 1

2 answers

The question did not come out as clear as it was typed. It is:

−3a + 4(x^5)b, x ≤ −1

ax − 2b −1, −1 < x < 1

3x^2 − bx + a, x ≥ 1
for f to be continuous, all three definitions must be equal at x=1. Since f is defined at x=1 in three different ways, we need

-3a+4b = a-2b-1
a-2b-1 = 3-b+a

So just solve those for a and b