Question

help with inverses

Answer 1

f(x)= 6-x^2 and g(x)= sqrt(6 - x)

f(g(x)) = 6-(sqrt(6 - x))^2 = 6 - (6 - x) = x

g(f(x) = sqrt(6 - (6-x^2)) = sqrt (x^2)

Answer 2

Not inverses because f is not 1 to 1.

Make a domain restriction for f and make it one to one.

f(x)= 6-x^2 for x >= 0

Since you are using the positive sqrt for the inverse.

Answer 3

Would this be the answer?