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

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

*f*(*x*) =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?*g*(*x*) =Consider the domain of each part of the subtraction problem separately.

*h*(*x*) =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*k*(*x*) =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