Functions $\mathrm{f}$ and $\mathrm{g}$ are defined by $\mathrm{f}:x\mapsto \frac{x+a}{x+b}$ for $x\

Question

Functions $\mathrm{f}$ and $\mathrm{g}$ are defined by $\mathrm{f}:x\mapsto \frac{x+a}{x+b}$ for $x\in \mathbb{R},$ $x
e -b,$ $a
e -1,$ $g:x\mapsto x$ for $x\in \mathbb{R}$. It is given that $\mathrm{ff}=g$. Find the value of $b$. Find ${{\mathrm{f}}^{-1}}(x)$ in terms of $x$ and $a$. [5]

Accepted Answer

$b = -1$; $\mathrm{f}^{-1}(x) = \dfrac{x+a}{x-1}$

N2018 P1 Q5

N2018 P1 Q5

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