Mathematics

Problem

For a fixed real number

a>1

, let

f(x)=\log_{a}x

and

g(x)=a^{x^{2}-9}

. a. (i) Find

(f\circ g)(x)

and state its domain. b. (ii) Show that

(f\circ g)(x)

is an even function. c. (iii) Determine the minimum value of

(f\circ g)(x)

and the least real value of

x

at which this minimum occurs.