Question 1

Paper 2, calculatorMedium5 marks

Let f(x)=1xf(x)=\dfrac{1}{x} x≠0x\ne 0 and define

g(x)=3+2f(x−1)=3x−1x−1,x≠1.g(x)=3+2f(x-1)=\frac{3x-1}{x-1},\qquad x\ne 1.
(a)

State the inverse function of ff

[1]
(b)

Hence determine g−1(x)g^{-1}(x) and state the equations of its vertical and horizontal asymptotes.

[4]

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