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# A2 C3 Maths Question, EX 2E, Q8 watch

1. The function f(x) is defined by f(x)= 2x^2-3 (x is a real number, x is smaller than 0). I have found the inverse to be Sqroot((x+3)/2)) which is correct. The second part of the question says... Find the values of a for which f(a)=f^(-1)(a)? Any help please! Thank you!
2. (Original post by E-V)
The function f(x) is defined by f(x)= 2x^2-3 (x is a real number, x is smaller than 0). I have found the inverse to be Sqroot((x+3)/2)) which is correct. The second part of the question says... Find the values of a for which f(a)=f^(-1)(a)? Any help please! Thank you!
f(x)=2x^2 -3
f(a)=2a^2 -3

f^(-1)(x)=[√(x+3)]/2
f^(-1)(a)=[√(a+3)]/2

Equate f(a) with f^(-1)(a) and solve to determine a
3. I put the two equal to each other and attempted to find a... I got two decimals 1.308.... and -1.433..., the answer in my book is -1. Is this right or have I done the maths wrong? Thank you for your help!
4. (Original post by E-V)
I put the two equal to each other and attempted to find a... I got two decimals 1.308.... and -1.433..., the answer in my book is -1. Is this right or have I done the maths wrong? Thank you for your help!
I cannot imagine where the decimals came from but x=-1 is certainly a solution to the quartic you get from putting those 2 equal to each other

What equation did you get
5. I managed it, silly mistake in the working! Thank you for your help x

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