If and are two distinct linear functions defined on such that they map onto

MATHEMATICS · Numerical · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

f

and

g

are two distinct linear functions defined on

\mathbb{R}

such that they map

[-1,1]

onto

[0,2]

, and

h:\mathbb{R}\setminus\{-1,0,1\}\to\mathbb{R}

is defined by

h(x)=\frac{f(x)}{g(x)}

, then

|h(h(x))+h(h(1/x))|>n

. Find the maximum integral value of

n