Question 1

Paper 1, no calculatorMedium5 marks

The graph of the function rr is shown in Figure 1. It is known that

r(x)=ax+bx+d,x≠−d,r(x)=\frac{ax+b}{x+d}, \qquad x\ne-d,

where a,b,d∈Ra,b,d\in\mathbb R

-4-3-2-1012344321-1-2-3-4(1,1)x=0y=0xy
(a)

Determine the values of aa bb and dd

[3]
(b)

Hence, show that rr is self-inverse, stating the domain of r−1r^{-1}

[2]

More AA 2.3 Rational, exponential and logarithmic functions questions