Function help

Question

If f(x)= √2x-4, what is f(f^-1(-4))? 

Answer 1

f(x)= √2x-4 <---- I'll assume that the entire radicand is (2x-4)

 

f^-1(x) = (x²+4)/2

 

f^-1(-4) however is not defined; here's why:

 

The domain of f is x≥2 and the range of f is y≥0.

The domain of f^-1 is the range of f, and the range of f^-1 is the domain of f;

therefore for the inverse of f, its domain is x≥0 and its range is y≥2.