Let and be continuous functions from to such that and

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

Problem

Let

f(x)

and

g(x)

be continuous functions from

\mathbb{R}

\mathbb{R}

such that

f(x_1)>f(x_2)

and

g(x_1)<g(x_2)

for all

x_1>x_2

. Find the solution set of

f(g(\alpha^2-2\alpha))>f(g(3\alpha-4))