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?

Question

Mathematics

Ishaan

11 July, 01:52

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?

+4

Answers (1)

Know the Answer?

Anastasia Austin · Answer 1

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

-1 x<=-1

ax-b - 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!

For what values of a and b is the following function is continuous at every x:-7 x ≤ - 3f (X) = ax-b - 3< x < 13 x ≥ 1Find the values is a and b ix f (x) continuous at every x?

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?