Find the domain f=(5x+4) / (x^2+3x+2)

Expert Answers info

hala718 eNotes educator | Certified Educator

calendarEducator since 2008

write3,662 answers

starTop subjects are Math, Science, and Social Sciences

f(x)= (5x+4)/(x^2+3x+2)

First we need to determine x values where f(x) is not defined.

f is not defined when x^2+3x+2 =0 (since f is a ratio)



x= {-1,-2}

Then f domain if R-{-1,-2}

check Approved by eNotes Editorial

tonys538 | Student

The domain of a function y = f(x) is the set of values x can take for which y is real and defined.

For the function f(x)=(5x+4)/(x^2+3x+2), the numerator is defined for all values of x. The function is indeterminate when the denominator x^2 + 3x + 2 is equal to 0. The values of x where this is the case have to be eliminated.

x^2 + 3x + 2 = 0

x^2 + 2x + x + 2 = 0

x(x + 2) + 1(x + 2) = 0

(x + 1)(x + 2) = 0

x = -1 and x = -2

At the values x = -1 and x = -2 the function y = f(x) is not defined.

This gives a domain of R - {-1, -2}

check Approved by eNotes Editorial
neela | Student

To find the domain of f(x) = (5x+4)/(x^2+3x+2).

Solution :

We shall find the values of  x for which the denominator x^2+3x+2 becomes zero. And for that x  the function becomes undefined with  a jump from -infinity to positive ifinity.

x^2+3x+2 = (x+2)(x+1) becomes zero when x+2 = 0 or x+1 = 0.  Or the denominator x^2+3x+2 bemes zero for x = -2 or x =-1.

So x wont take values -2 and -1. And x tacan take any other real values.


check Approved by eNotes Editorial
giorgiana1976 | Student

We'll establish the domain knowing the fact that the division by 0 is not allowed.

For this reason, we'll find out first, the x values for the denominator is cancelling.

To find out these values, we'll have to calculate the roots of the quadratic equation from the denominator.







From here we conclude that the function is not defined for x=-1 and x=-2.

So, the domain of definition is: R - {-2;-1}

check Approved by eNotes Editorial