Asked by Mia
Verify that the functions f and g, are inverses of each other by showing that
f(g(x))=x and g(f(x))=x.
f(x)=4-x^3
g(x)=^3ã4-x
f(g(x))=x and g(f(x))=x.
f(x)=4-x^3
g(x)=^3ã4-x
Answers
Answered by
Steve
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
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