Practicing Success
If f and g are two increasing functions such that gof is defined, then |
gof is an increasing function gof is a decreasing function gof is neither increasing nor decreasing None of these |
gof is an increasing function |
Let $x_1, x_2 \in R$ such that $x_1<x_2$ $\Rightarrow f\left(x_1\right)<f\left(x_2\right)$ (∵ f is increasing) $\Rightarrow g\left(f\left(x_1\right)\right)<g\left(f\left(x_2\right)\right)$ (∵ g is increasing) $\Rightarrow(gof)\left(x_1\right)<(gof)\left(x_2\right)$ ⇒ gof is increasing. |