The function $$\(\mathrm{f}\)$$ is defined as follows: $$\[ f(x)=\frac{x+3}{x-1} \text { for } x> 1 . \]$$ Find an expression for $$\(\mathrm{f}^{-1}(x)\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w21_qp_12 Year：2021 Question No：3(b)
Answer:
\(\frac{x+3}{x-1}=y \Rightarrow x+3=x y-y\) OR \(\frac{y+3}{y-1}=x \Rightarrow y+3=x y-x\)
\(x y-x=y+3 \Rightarrow x=\frac{y+3}{y-1}\) OE OR \(y+3=x y-x \Rightarrow y=\left[\frac{x+3}{x-1}\right] \mathrm{OE}\)
\(\left[\mathrm{f}^{-1}(x)\right.\) or \(\left.y\right]=\frac{x+3}{x-1}\)
\(x y-x=y+3 \Rightarrow x=\frac{y+3}{y-1}\) OE OR \(y+3=x y-x \Rightarrow y=\left[\frac{x+3}{x-1}\right] \mathrm{OE}\)
\(\left[\mathrm{f}^{-1}(x)\right.\) or \(\left.y\right]=\frac{x+3}{x-1}\)
Knowledge points:
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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