How to Solve Irrational Functions?

Irrational functions are generally considered to be functions that have a radical sign. In this post, you will learn more about the definition of irrational functions.

How to Solve Irrational Functions?

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Step-by-step guide to irrational functions

An irrational function can be said to be a function that cannot be written as the quotient of two polynomials, but this definition is not usually used. In general, the most commonly used definition is that an irrational function is a function that contains variables in the radicals, i.e., square roots, cube roots, etc.

Therefore, the fundamental form of an irrational function is:

\(\color{blue}{f\left(x\right)=\sqrt[n]{\left(g\left(x\right)\right)^m}}\) or \(\color{blue}{f\left(x\right)=\left(g\left(x\right)\right)^{\left(\frac{m}{n}\right)}}\)

Where, \(g(x)\) is a rational function.

  • If the index \(n\) of the radical is odd, it is possible to calculate the domain of all real numbers.
  • If the index \(n\) of the radical is even, we need \(g(x)\) to be positive or zero since the even roots of a negative number are not real.

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