Algebra of functions

Question

Find the domain of the function

f(x) = 6⁄x-7

Answer 1

Since you did not use parenthesis, I have to guess what you mean. I'm guessing this:

If indeed this is your problem, then the domain is restricted by the fact that division by zero is not defined. So, since we are not allowed to have the denominator equal to zero, we can say:

x - 7 ≠ 0 and adding 7 to both sides gives:

x ≠ 7

So, "x" can be any real number except 7. You can relate that using many methods and here are a few:

1. The domain is all real numbers except 7
2. The domain is -∞ < x < 7 U 7 < x < ∞
3. The domain is {x| -∞ < x < 7 or 7 < x < ∞}
4. The domain is (-∞, 7) U (7, ∞)