# Math Help - calc help

1. ## calc help

f(x) = {(x^2-4)/(x-2) if x<2}
{ax^2-bx-3 if 2<x<3}
{2x-a+b if x >= 3}

They are all part of the same function...the problem is to find the values of a and b to make the entire function continuous. I got a and b is equal to .5, could anyone help me on this please?

thanks.

2. Originally Posted by amma0913
f(x) = {(x^2-4)/(x-2) if x<2}
{ax^2-bx-3 if 2<x<3}
{2x-a+b if x >= 3}

They are all part of the same function...the problem is to find the values of a and b to make the entire function continuous. I got a and b is equal to .5, could anyone help me on this please?

thanks.
Note that $\frac{x^2 - 4}{x - 2} = x + 2$ for $x \neq 2$.

So for continuity at x = 2 you require the following: $2 + 2 = 4a - 2b - 3$.

For continuity at x = 3 you require $9a - 3b - 3 = 6 - a + b$.

Simplify each of the above equations and solve them simultaneously for a and b.