The functions $\mathrm{f}$ and $\mathrm{f}{{\mathrm{g}}^{-1}}$ are defined as follows: $\mathrm{f}:x

Question

The functions $\mathrm{f}$ and $\mathrm{f}{{\mathrm{g}}^{-1}}$ are defined as follows: $\mathrm{f}:x\mapsto x+5, x\in \mathbb{R}$ $\mathrm{f}{{\mathrm{g}}^{-1}}:x\mapsto {{x}^{2}}$, $x\in \mathbb{R}$, $x>\sqrt{5}$. Find the functions $\mathrm{g}$ and $\mathrm{fg}$. The function $\mathrm{h}$ is defined such that its inverse exists and the graphs of $y=\mathrm{f}\left( x \right)$ and $y={{\mathrm{h}}^{-1}}\left( 3x+1 \right)$ are symmetrical about the line $y=x$. Find $\mathrm{h}\left( x \right)$.

Accepted Answer

(i) $\mathrm g:x\mapsto\sqrt{x+5}$, $x>0$, and $\mathrm{fg}:x\mapsto\sqrt{x+5}+5$, $x>0$ (ii) $\mathrm h(x)=3x+16$

RI Functions Tutorial Q13

RI Functions Tutorial Q13

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