Consider the function

MATHEMATICS · Multi-part · AoPS · Mathematics · Functions · Functions

Problem

f_a(x)=\sqrt{x+a}

, where

a\in\mathbb R

. (i) Define the domain of a real-valued function of a real variable. (ii) Write the domain of

f_a

in set-builder form in terms of

a

. (iii) If

2

belongs to the domain of

f_a

but

-5

does not, determine all possible real values of

a

, showing each step clearly.