C3 inverse functions help Watch

ZettaLost
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This question is from the edexcel C3 book, 2nd chapter (functions)

The function f(x) is defined by f(x)= 2x^2 −3 {x∈ℝ,x<0}. Determine
(a) f^−1(x) clearly stating its domain

So what I did was


Let y= 2x^2 −3
y+3= 2x^2


(y+3)/2 = x^2

x = + / - sqrt. ( (y+3)/2 )

f^−1(x) = + / - sqrt. ( (x+3)/2 )

The domain is going to be the range of f(x), so for f^−1(x): x∈ℝ,x>−3


But the answer is f^−1(x) is only the negative square root.
f^−1(x): - sqrt. ((x+3)/2), x∈ℝ,x>−3

I don't understand why we discard the positive square root? :confused:
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brianeverit
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(Original post by ZettaLost)
This question is from the edexcel C3 book, 2nd chapter (functions)

The function f(x) is defined by f(x)= 2x^2 −3 {x∈ℝ,x<0}. Determine
(a) f^−1(x) clearly stating its domain

So what I did was


Let y= 2x^2 −3
y+3= 2x^2


(y+3)/2 = x^2

x = + / - sqrt. ( (y+3)/2 )

f^−1(x) = + / - sqrt. ( (x+3)/2 )

The domain is going to be the range of f(x), so for f^−1(x): x∈ℝ,x>−3


But the answer is f^−1(x) is only the negative square root.
f^−1(x): - sqrt. ((x+3)/2), x∈ℝ,x>−3

I don't understand why we discard the positive square root? :confused:
Have you taken account of the fact that f(x) is only defined for x>0 ?
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ZettaLost
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(Original post by brianeverit)
Have you taken account of the fact that f(x) is only defined for x>0 ?
You mean x<0?
Oh I think I get it. Basically the domain of f(x) is negative, so the range of f^-1(x) should also be negative? Thank you!
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brianeverit
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(Original post by ZettaLost)
You mean x<0?
Oh I think I get it. Basically the domain of f(x) is negative, so the range of f^-1(x) should also be negative? Thank you!
Yes I meant x<0. Just a typo.
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