Mathematics

Problem

Let

f_a(x)=\sqrt{x^{2}-4ax+4a^{2}-1},

where

a

is a real parameter. a. (i) For a fixed

a

, write the condition on the quadratic expression inside the square root that guarantees real values of

f_a(x)

. b. (ii) Using the result of part (i), determine all real values of

a

for which the domain of

f_a

is non-empty. c. (iii) For each value (or range) of

a

obtained in part (ii), describe the corresponding domain of

f_a