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]

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