Algebra help needed in Inverse functions: Problems type 3 and interval notation

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The one-to-one function f is defined here:  f(x)=√2x-2

Find f⁻¹, the inverse of f.

Then give the domain of f⁻¹ using interval notation

Nov 1st, 2015

Thank you for the opportunity to help you with your question!

The answer :

we have :  f(x) = sqrt(2x - 2)

so to find the inverse of the function should put :  y = sqrt(2x - 2) 

so  :  y² = 2x - 2

so :   y² + 2 = 2x

so :  x = y²/2 + 1

so :  f^-1(x) = (1/2)y² + 1

the domain is :  IR

interval natation is :  Df^-1 = ]-infinity , 0] U [0 , +infinity[ 

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Nov 1st, 2015

so I would write it like this:  f⁻¹(x)=1/2 and then the domain of f⁻¹=(⁻∞,0)(0,⁺∞) 

Nov 1st, 2015

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