How to Combine Two Related Formulas into One in Mathematics?

[lenfromkits]

I have a situation where I have two formulas that relate together but do not really transition from one to the other and I'm not sure how to properly write this as a single formula.

I have these two cases:
when \ b<100: a=b*4

when \ b>=100: a=\frac{b}{4}


I just need a nicer more professional way of writing that as one formula.

Thanks.

 

[JHamm]

a(b) = \left\{\begin{array}{cc}4b, &\mbox{ if } b < 100\\ \frac{b}{4}, &\mbox{ if } b \geq 100\end{array}\right.

For more information check out http://mathworld.wolfram.com/PiecewiseFunction.html

 

[lenfromkits]

Perfect. Thank you!

 

[HallsofIvy]

Or, if you prefer it on one line,
a(b)= 4b+ \left(\frac{4}{b}- 4b\right)H(b- 100)
where H(x) is the "Heviside step function" which is 0 for x< 0, 1 for x\ge 0.

 

[JHamm]

You math kids, and just as I was feeling clever too...