Domain of Rational Functions...2

[nycmathguy]

Find domain of f(x) = [(x - 4)/(x - 10)] + 4

Is the first step to combine the fractions?

[(x - 4)/(x - 10)] + (4/1)

LCD = (x - 10)

[(x - 4) - 4(x - 10)]/(x - 10)

[(x - 4) - 4x + 40)]/(x - 10)

(-3x + 36)/(x - 10)

I see that it really does not make a difference if I combine the fractions or not.

Set denominator to 0 and solve for x.

x - 10 = 0

x = 10

Let R = all real numbers.

Domain = R except x cannot be 10.

How is this written in interval and inequality notation?

 

[MathLover1]

correct

interval notation: (-infinity, 10) U (10, infinity)

 

[nycmathguy]

correct

interval notation: (-infinity, 10) U (10, infinity)

Very good.