The functions $$$\mathrm{f}$$$ and $$$\mathrm{g}$$$ are defined by $$\[ \begin{array}{ll} \mathrm{f}(x)=x^{2}+3 & \text { for } x> 0 \\ \mathrm{~g}(x)=2 x+1 & \text { for } x> -\frac{1}{2} \end{array} \]$$ Find an expression for $$$(\mathrm{fg})^{-1}(x)$$$ and state the domain of (fg) $$$)^{-1}$$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_11 Year：2020 Question No：11(b)

Answer:

$y=(2 x+1)^{2}+3 \rightarrow 2 x+1=(\pm) \sqrt{y-3}$
$x=(\pm) \frac{1}{2}(\sqrt{y-3}-1)$
$\left(\operatorname{fg}^{-1}(x)=\right) \frac{1}{2}(\sqrt{x-3}-1)$ for $(x)> 3$

Knowledge points:

1.2.1 understand the terms function, domain, range, one-one function, inverse function and composition of functions

1.2.3 determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases

Answer:

Knowledge points:

Solution:

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