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

2 Answers
Jim G.
Jul 29, 2018

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]}

Jacobi J.
Jul 30, 2018

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!

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