Problem

Which of the following are rational functions? Select all that apply. $f(x)=\frac{x^{5}-x^{3}+4}{x^{2}+15 x-2}$ $f(x)=\frac{1}{x}$ $f(x)=\frac{2^{x}}{5}$ $f(x)=\frac{x^{2}+5}{x}$ $f(x)=\frac{\log (x)}{2 x+5}$

Solution

Step 1 :A rational function is a function that can be written as the ratio of two polynomials. The numerator and the denominator are both polynomials. The denominator cannot be zero.

Step 2 :Looking at the functions given, we can see that \(f(x)=\frac{x^{5}-x^{3}+4}{x^{2}+15 x-2}\), \(f(x)=\frac{1}{x}\), and \(f(x)=\frac{x^{2}+5}{x}\) are rational functions because they can be written as the ratio of two polynomials.

Step 3 :\(f(x)=\frac{2^{x}}{5}\) and \(f(x)=\frac{\log (x)}{2 x+5}\) are not rational functions because \(2^{x}\) and \(\log (x)\) are not polynomials.

Step 4 :\(\boxed{\text{The rational functions are } f(x)=\frac{x^{5}-x^{3}+4}{x^{2}+15 x-2}, f(x)=\frac{1}{x}, \text{ and } f(x)=\frac{x^{2}+5}{x}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/20334/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download