what is an "explicit" forumla in mathematics?

Question

i always see questions asking to write an explicit formula for ..... whats the difference between explicit and implicit? thanks!

Answer 1

An explicit formula or function is one where you can directly compute the value of it for a given value of its variable(s). For example, the following is an explicit formula:

√(1-x²)

However, an implicit formula doesn't yield a value so directly, and frequently requires solving for another variable even if a value is given for one variable. For example, the following is an implicit formula:

x² + y² = 1

Both are actually the same thing, which is a circle, but notice that while the first is easy to compute for various values of x, the other is not so straightforward. You might think that the other isn't so hard to do, but there are plenty of implicit functions than can be downright insoluble, such as:

Sin(xy) + xy = 0

Good luck with that one! Let's see you try plotting it.