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# last maths question i promise! watch

1. sry everyone, last maths question i promise.

let f(x) = x^2 - 2x + 3 x ER x > or equal to 1

a) by completin the square sketch the graph y = f(x) for x > or equal to 1.

I have done this, but i think I've got it wrong. i got 1 + or - root2

b) state the range of f

c) find the inverse finction stating its domain and range.

i've done this one too. for the inverse I got y - 3 / -2 x ER x > or equal to 1.

I'm just really checking my answers here coz I'm not really sure if they are right. I missed quite a few of the lessons on this through illness and havn't really had a chance to catch up (i'm tryin) , so cheers for any help!
2. (Original post by ainat87)
let f(x) = x^2 - 2x + 3 x ER x > or equal to 1

a) by completin the square sketch the graph y = f(x) for x > or equal to 1.
f(x) = (x-1)² +2

this is an x² parabola shifted right 1, with its minimum at x=1 (i.e. at the lower bound of the domain) and shifted up 2. (i.e. its minimum is (1,2))

b) state the range of f
f>=2

c) find the inverse finction stating its domain and range.
let g(x) = f^{-1}(x) for layout simplicity

by geometry, g(x) = √(x-2) +1; x Є R; x >= 2.

range: g(x) >= 1

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