Question

If $f$ and $g$ are two increasing function such that $fog$ is defined, then $fog$ will be

• A. increasing function
• B. decreasing function
• C. neither increasing nor decreasing
• D. None of these

Answer 1

The correct option is A increasing function

Let $x_1,x_2\in R$ such that $x_1<x_2$ then
$\Rightarrow g\left(x_1\right)>g\left(x_2\right)$ ($\because g$ is an increasing function )
$\Rightarrow f\left(g\right(x_1\left)\right)<f\left(g\right(x_2\left)\right)$ ($\because f$ is an increasing function)
$\Rightarrow fog\left(x_1\right)<fog\left(x_2\right)$
Hence, $fog$ is an increasing function.