An inverse equation with a restriction

An inverse equation with a restriction

5 marks

TGM Original

Let f(x)=2+ 3x, x>0. Find f-1(x) with its domain. Solve f-1(x)=x-2, rejecting any invalid root.

Solution:

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Answer:\(\mathrm f^{-1}(x)=\dfrac3{x-2}\), \(x>2\); solution \(x=2+\sqrt3\).

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