2016 VCE Maths Methods Mini Test 5
Number of marks: 9
Reading time: 2 minutes
Writing time: 13 minutes
Instructions – No Calculator
• Answer all questions in the spaces provided.
• Write your responses in English.
• In questions where a numerical answer is required, an exact value must be given unless otherwise specified.
• In questions where more than one mark is available, appropriate working must be shown.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Let \(f: (0, \infty) \to R\), where \(f(x) = \log_e(x)\) and \(g: R \to R\), where \(g(x) = x^2+1\).
a.
i. Find the rule for \(h\), where \(h(x) = f(g(x))\). 1 mark
ii. State the domain and range of \(h\). 2 marks
iii. Show that \(h(x) + h(-x) = f((g(x))^2)\). 2 marks
iv. Find the coordinates of the stationary point of \(h\) and state its nature. 2 marks
b. Let \(k: (-\infty, 0] \to R\), where \(k(x) = \log_e(x^2+1)\).
i. Find the rule for \(k^{-1}\). 2 marks
ii. State the domain and range of \(k^{-1}\). 2 marks
End of examination questions
VCE is a registered trademark of the VCAA. The VCAA does not endorse or make any warranties regarding this study resource. Past VCE exams and related content can be accessed directly at www.vcaa.vic.edu.au
