The functions $\mathrm{f}$ and $\mathrm{g}$ are defined by \(\begin{align} & \mathrm{f}:x\mapsto

Question

The functions $\mathrm{f}$ and $\mathrm{g}$ are defined by $\begin{align} & \mathrm{f}:x\mapsto {{x}^{2}}+2x-3,\quad x>-3 \ & \mathrm{g}:x\mapsto 3x-2,\quad x\ge 0 \ \end{align}$ Show that $\mathrm{fg}$ exists and find $\mathrm{fg}$, stating its domain. Find the range of $\mathrm{fg}$.

Accepted Answer

$fg:x\mapsto9x^2-6x-3$, $x\ge0$, $R_{fg}=[-4,\infty)$

Functions - Composite Functions

Functions - Composite Functions

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