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

State the domain for each of the functions below.

is excluded from the denominator of a fraction because division by would make the fraction *undefined*. What value of, if any, would make the denominator?

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

has a domain of while has a domain of . Since

is the difference between and , both excluded values must be excluded from .

Typically, a square root function has a domain of

, but in this case,is squared... meaning both positive or negative values will yield positive outputs. However, do not neglect to consider the. What values of , both positive and negative, will make?

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

What is the domain of

?

What is the domain of

?

What value is excluded from the denominator of all fractions?

Now combine these results to find the domain of

.