Question 1

Paper 2, calculatorMedium7 marks

The function gg is defined by

g(x)=2x+3x−2,x∈R, x≠2.g(x)=\frac{2x+3}{x-2},\qquad x\in\mathbb{R},\ x\ne2.
(a)

State the equations of the vertical and horizontal asymptotes of the graph of gg

[2]
(b)

Sketch the graph of gg showing and labelling its asymptotes and its intercepts with the axes.

[3]
(c)

Determine g−1(x)g^{-1}(x) including its domain, and hence state whether gg is self-inverse.

[2]

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