Question

Let f(x) and g(x) be two continuous functions defined from $R\to R$, such that $f\left(x_1\right)>f\left(x_2\right)$ and $g\left(x_1\right)<g\left(x_2\right),\forall x_1>x_2$ then solution set of $f\left(g\right({\alpha }^2-2\alpha \left)\right)>f\left(g\right(3\alpha -4\left)\right)$ is

• A. R
• B. $\Phi$
• C. $(1,4)$
• D. $R-[1,4]$

Answer 1

The correct option is C $(1,4)$

$f\left(g({\alpha }^2-2\alpha )\right)>f\left(g(3\alpha -4)\right)⟹g({\alpha }^2-2\alpha )>g(3\alpha -4)⟹{\alpha }^2-2\alpha <3\alpha -4$
$(\alpha -1)(\alpha -4)<0$
$1<\alpha <4$
$⟹\alpha ϵ(1,4)$
Hence, option 'C' is correct.