The functions $$\(\mathrm{f}\)$$ and $$\(\mathrm{g}\)$$ are defined by $$\[ \begin{aligned} & \mathrm{f}(x)=x^{2}-4 x+3 \text { for } x> c, \text { where } c \text { is a constant, } \\ & \mathrm{g}(x)=\frac{1}{x+1} \text { for } x> -1 \end{aligned} \]$$ It is now given that $$\(c=5\)$$. Find an expression for $$\(\mathrm{f}^{-1}(x)\)$$ and state the domain of $$\(\mathrm{f}^{-1}\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_s20_qp_13 Year：2020 Question No：9(c)
Answer:
\(y=(x-2)^{2}-1 \rightarrow(x-2)^{2}=y+1\)
\(x=2(\pm) \sqrt{y+1}\)
\(\left(\mathrm{f}^{-1}(x)\right)=2+\sqrt{x+1}\) for \(x> 8\)
\(x=2(\pm) \sqrt{y+1}\)
\(\left(\mathrm{f}^{-1}(x)\right)=2+\sqrt{x+1}\) for \(x> 8\)
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
Solution:
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