IB Maths AA SL AA 2.1 Lines, functions and graphs questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper
Paper 1, no calculatorPaper 2, calculator
Difficulty
EasyMediumHard

Question 1

Paper 1, no calculatorMedium6 marks

The function ff is defined by

f(x)=(x−2)2+1,x≥2.f(x)=(x-2)^2+1,\qquad x\geq 2.
(a)

Explain why ff has an inverse function.

[1]
(b)

Find f−1(x)f^{-1}(x) stating its domain.

[3]
(c)

Using your answer to (b), determine (f−1∘f)(5)(f^{-1}\circ f)(5) showing the value of f(5)f(5)

[2]