Let and be real-valued functions defined on subsets of .

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Let

f

and

g

be real-valued functions defined on subsets of

\mathbb{R}

. (i) Define

(f+g)(x)

and

(f-g)(x)

. (ii) If

\operatorname{Dom}(f)=A

and

\operatorname{Dom}(g)=B

, explain with reason what the domain of

f+g

should be. (iii) Give one explicit example of two functions

f

and

g

such that

\operatorname{Dom}(f)=\mathbb{R}\setminus\{2\}

and

\operatorname{Dom}(g)=\mathbb{R}\setminus\{-3\}

, and write the domain of

f+g

for your example.