The diagram shows the graph of $$\(y=\mathrm{f}(x)\)$$. Find an expression for $$\(\mathrm{f}^{-1}(x)\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w21_qp_13 Year：2021 Question No：6(b)
Answer:
\(y=\frac{-x}{\sqrt{4-x^{2}}}\) leading to \(x^{2}=y^{2}\left(4-x^{2}\right)\)
\(x^{2}\left(1+y^{2}\right)=4 y^{2}\)
\(x=(\pm) \frac{2 y}{\sqrt{1+y^{2}}}\)
\(\mathrm{f}^{-1}(x)=\frac{-2 x}{\sqrt{1+x^{2}}}\)
\(x^{2}\left(1+y^{2}\right)=4 y^{2}\)
\(x=(\pm) \frac{2 y}{\sqrt{1+y^{2}}}\)
\(\mathrm{f}^{-1}(x)=\frac{-2 x}{\sqrt{1+x^{2}}}\)
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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