3.12: Completing the square and inverse of a quadratic

0606/12/F/M/25 — Question 5 · 8 marks

(a)

Write

2x^{2}-2x+3

in the form

a(x+b)^{2}+c

, where

a

,

b

and

c

are constants.

[3]

(b)

It is given that

\mathrm{f}(x)=2x^{2}-2x+3

for

x\leqslant p

. Write down the greatest value of

p

for which

\mathrm{f}

has an inverse.

[1]

(c)

Using this value of

p

, write down the range of

\mathrm{f}

.

[1]

(d)

Using this value of

p

, find an expression for

\mathrm{f}^{-1}(x)

.

[3]