Composite of Functions
A function is performed, and then a second function is performed on the result of the first function. The composition of f and g is denoted by f(g), and [f(g)](x)=f[g(x)].
Binomials of the form a(square root of b)+c(square root of d) and a(square root of b)-c(square root of d), where a, b, c, and d are rational numbers.
A number that does not satisfy the original equation.
The function I(x)=x.
Two functions f and g are in inverse functions if and only it both of their compositions are the identity function.
Like Radical Expressions
Two radical expressions in which both the radicands and indices are alike.
For any real numbers a and b, and any positive integer, if a^n=b, then a is an nth root of b.
1. A function where each element of the range is paired with exactly one element of the domain. 2. A function whose inverse is a function.
The nonnegative root.
An equation with radicals that have variables in the radicand.
An inequality that has a variable in the radicand.
Rationalizing the Denominator
To eliminate radicals from a denominator or fractions from a radicand.
Square Root Function
A function that contains a square root of a variable.
Square Root Inequality
An inequality involving square roots.