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