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

State the domain for each of the functions below.

We all know that

is excluded from the denominator of a fraction. What value of , if any, would make the denominator?

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

Sinceis 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.

I. What is the domain of?

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

IV. Now combine these results to find the domain of.I.

II.

III.

IV.