contestada

if f^-1(y) is the inverse of f(x) which statements must be true?

A) F(F^-1(x))=x
B) F^-1(F(x))=x
C) The range of f^-1(y) is the range of f(x)
D) The range of F^-1(y) is the domain of F(x)
E) The domain of F^-1(y) is the range of F(x)
F) The domain of F^-1(y) is the domain of F(x)

Respuesta :

scme1702
Let us assume f(x) = 2x - 5
f⁻¹(x) = (x + 5)/2
f(f⁻¹(x)) = 2((x + 5)/2) - 5 = x
f⁻¹(f(x)) = (2x - 5 + 5)/2 = x
The domain of a function is the range of its inverse and vice versa
The range of a function is the domain of its inverse and vice versa
Therefore, statements A, B, D and E are true

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