Given the function #g(x)=(x^2-3x-4)/(x-5)#, how do you find the domain?

2 Answers
Jul 29, 2018

Answer:

#x inRR,x!=5#

Explanation:

The denominator of g(x) cannot be zero as this would make g(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

#"solve "x-5=0rArrx=5larrcolor(red)"excluded value"#

#"domain is "x inRR,x!=5#

#(-oo,5)uu(5,oo)larrcolor(blue)"in interval notation"#
graph{(x^2-3x-4)/(x-5 [-40, 40, -20, 20]}

Jul 30, 2018

Answer:

#x inRR, x!=5#

Explanation:

The only #x# value that will make this function undefined is when the denominator is set to zero. We see that this value is #x=5#.

Therefore, we can say that the domain is #x inRR, x!=5#. This is just a fancy way of saying #x# can be any real number except #5#.

We also see this graphically, as we have a vertical asymptote at #x=5#.

graph{(x^2-3x-4)/(x-5) [-74, 86, -36.8, 43.2]}

Hope this helps!