Functions $$\(\mathrm{f}\)$$ and $$\(\mathrm{g}\)$$ are defined by $$\[ \begin{array}{ll} \mathrm{f}(x)=4 x-2, & \text { for } x \in \mathbb{R}, \\ \mathrm{g}(x)=\frac{4}{x+1}, & \text { for } x \in \mathbb{R}, x \neq-1 . \end{array} \]$$ Find the values of $$\(x\)$$ for which $$\(\mathrm{f}^{-1}(x)=\mathrm{g}^{-1}(x)\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w20_qp_12 Year：2020 Question No：5(b)
Answer:
\(\left(\mathrm{f}^{-1}(x)\right)=\frac{x+2}{4},\left(\mathrm{~g}^{-1}(x)\right)=\frac{4-x}{x}\) or \(\frac{4}{x}-1\)
\(x^{2}+6 x-16(=0)\)
\((x+8)\) and \((x-2)\)
\((x=) 2\) or \(-8\)
\(x^{2}+6 x-16(=0)\)
\((x+8)\) and \((x-2)\)
\((x=) 2\) or \(-8\)
Knowledge points:
1.1.3 solve quadratic equations, and quadratic inequalities, in one unknown (By factorising, completing the square and using the formula.)
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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