Verify that the functions f and g, are inverses of each other by showing that

Question

f(g(x))=x and g(f(x))=x.

f(x)=4-x^3
g(x)=^3�ã4-x

Answer 1

just plug in the values for f and g

f(g) = 4 - g^3 = 4 - cbrt(4-x)^3 = 4 - (4-x) = x

g(f) = cbrt(4-f) = cbrt(4 - (4-x^3)) = cbrt(4-4+x^3) = cbrt(x^3) = x