Additional Mathematics – Functions | e-Consult
Functions (1 questions)
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Let \(y = \dfrac{2x+5}{x-1}\). Solve for \(x\):
\(y(x-1)=2x+5\)
\(yx - y = 2x + 5\)
\(yx - 2x = y + 5\)
\(x(y-2)=y+5\)
\(x = \dfrac{y+5}{\,y-2\,}\).
Interchanging \(x\) and \(y\) yields
\(g^{-1}(x)=\dfrac{x+5}{\,x-2\,}\), Domain: \(x\neq 2\).