Let and , where the square roots denote principal (non-negative) values. Answer the…

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

Problem

Let

f(x)=\sqrt{3-2x}

and

g(x)=\sqrt{x+1}

, where the square roots denote principal (non-negative) values. Answer the following questions. (i) Find the domain of

f

and the domain of

g

. (ii) Determine the domain of the sum function

(f+g)(x)

. (iii) Justify, with reference to the defining rules of

f

and

g

, why every element outside the set obtained in part (ii) must be excluded from the domain of

(f+g)(x)