For a fixed real number

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

a>1

, let

f(x)=\log_{a}x

and

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

. (i) Find

(f\circ g)(x)

and state its domain. (ii) Show that

(f\circ g)(x)

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

(f\circ g)(x)

and the least real value of

x

at which this minimum occurs.