### Home > CALC > Chapter 1 > Lesson 1.2.2 > Problem 1-40

State the domain for each of the functions below. Homework Help ✎

We all know that 0 is excluded from the denominator of a fraction. What value of *x*, if any, would make the denominator *x*^{2} + 1 = 0?

Consider the domain of each part of the subtraction problem separately.

Typically, a square root function has a domain of *x* ≥ 0, but in this case, *x* is squared... meaning both positive or negative values will yield positive outputs. However, do not neglect to consider the − 9.

What values of *x*, both positive and negative, will make *x*^{2} − 9 > 0?

*x* ≤ − 3 U *x* ≥ 3

Consider the domain of the numerator and the domain of the denominator separately.

I. What is the domain of log(*x* − 3)?

III. What value is excluded from the denominator of all fractions?

IV. Now combine these results to find the domain of *k*(*x*).

I. *x* > 3

II. *x* ≥ −4

III. *x* ≠ −4

IV. *x* > 3