a) The function f x 2x 12x 8 is defined for x R i) Express f(x) in the form a(x b) c, where a, b and care constants ii) Find the range of f(x) b) The function g x 2x 12x 8 is defined for x D i) Find the smallest value of D for which g has an inverse ii) For this value of D, find an expression for g...

a i Completing the square fx 2x 6x 4 0 fx 2x 3 2 So a 2 b 3 and c 2 ii Since the coefficient of x is ...

a) The function f: x 2x 12x + 8 is defined for x R.

Question:

a) The function f: x ↦ 2x² − 12x + 8 is defined for x ∈ R.

i) Express f(x) in the form a(x + b)² + c, where a, b and care constants.

ii) Find the range of f(x).

b) The function g: x ↦ 2x² − 12x + 8 is defined for x ≥ D.

i) Find the smallest value of D for which g has an inverse.

ii) For this value of D, find an expression for g⁻¹(x) in terms of x.

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Complete Pure Mathematics 1 For Cambridge International AS & A Level

ISBN: 9780198427438

2nd Edition

Authors: Jean Linsky, Brian Western, James Nicholson

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Question Posted: Apr 13, 2023 10:48 AM

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a) The function f: x 2x 12x + 8 is defined for x R.

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a i Completing the square fx 2x 6x 4 0 fx 2x 3 2 So a 2 b 3 and c 2 ii Since the coefficient of x is ...View the full answer

Complete Pure Mathematics 1 For Cambridge International AS & A Level

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