19N.2.AHL.TZ0.H_3

pestleMathematicsAAHLPaper 219N· sl-2-2-functions-notation-domain-range-and-inverse-as-reflectionsource ↗

The following diagram shows the graph of $y = f\left( x \right)$ , $- 3 \leqslant x \leqslant 5$ .

Find the value of $\left( {f \circ f} \right)\left( 1 \right)$ .

[2]

Given that ${f^{ - 1}}\left( a \right) = 3$ , determine the value of $a$ .

[2]

Given that $g\left( x \right) = 2f\left( {x - 1} \right)$ , find the domain and range of $g$ .

[2]

Markscheme / solution

$f\left( 1 \right) = 0$ (A1)

$f\left( 0 \right) = - 1$ A1

[2 marks]

$a = f\left( 3 \right)$ (M1)

$\Rightarrow a = 4$ A1

[2 marks]

domain is $- 2 \leqslant x \leqslant 6$ A1

range is $- 6 \leqslant y \leqslant 10$ A1

[2 marks]

Examiners’ report

[N/A]