The values of x for which the rational expression is undefined are -6 and -8.
<h3>What is a function?</h3>
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a rational function:
![\rm f(x) = \dfrac{3x+20}{x^2+14x+48}](https://tex.z-dn.net/?f=%5Crm%20f%28x%29%20%3D%20%5Cdfrac%7B3x%2B20%7D%7Bx%5E2%2B14x%2B48%7D)
As we know in the rational function denominator cannot be zero:
The values of x for which the rational expression is undefined.
x² + 14x + 48 = 0
![\rm x_{1,\:2}=\dfrac{-14\pm \sqrt{14^2-4\cdot \:1\cdot \:48}}{2\cdot \:1}](https://tex.z-dn.net/?f=%5Crm%20x_%7B1%2C%5C%3A2%7D%3D%5Cdfrac%7B-14%5Cpm%20%5Csqrt%7B14%5E2-4%5Ccdot%20%5C%3A1%5Ccdot%20%5C%3A48%7D%7D%7B2%5Ccdot%20%5C%3A1%7D)
![\rm x_1=\dfrac{-14+2}{2\cdot \:1},\:x_2=\dfrac{-14-2}{2\cdot \:1}](https://tex.z-dn.net/?f=%5Crm%20x_1%3D%5Cdfrac%7B-14%2B2%7D%7B2%5Ccdot%20%5C%3A1%7D%2C%5C%3Ax_2%3D%5Cdfrac%7B-14-2%7D%7B2%5Ccdot%20%5C%3A1%7D)
x = -6, -8
Thus, the values of x for which the rational expression is undefined are -6 and -8.
Learn more about the function here:
brainly.com/question/5245372
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