Find the Domain of the function.(Enter your answers using interval notation).

Question

Find the domain of the function. (Enter your answers using interval notation.)

(a)

f(x) =

36 − x

(−∞,∞)

 

(b)

f(x) = x + 7

6x2 − x − 7

Answer 1

It's hard to tell what the functions are by your question. I'm guessing that the function for question a) is:

If so, the domain is restricted by the fact that you can only take the square root of a number zero or larger. There is no real number for the square root of a negative number. Therefore:

36 - x > 0

-x > -36

x < 36

In interval notation, this is (-∞, 36]

I'm also guessing that the function for question 2 is:

The domain of this function is limited by the fact that the denominator cannot equal zero (dividing by zero is not defined).

So 6x² - x - 7 ≠ 0

(6x - 7)(x + 1) ≠ 0

So 6x - 7 ≠ 0 or x ≠ 7/6

And x + 1 ≠ 0 or x ≠ -1

In interval notation this is (-∞, -1) U (-1, 7/6) U (7/6, ∞)