How do you find the function compositions given g(x)=x^2-2 and h(x)=sqrt(5-x)?

1 Answer
Jan 11, 2016

g(h(x)) = 3 - x

h(g(x)) = sqrt(7 - x^2)

Explanation:

g(h(x)) = g(sqrt(5 - x ) ) = (sqrt(5 - x ))^2 - 2 = 5 - x - 2 =
= 3 - x

h(g(x)) = h(x^2 - 2 ) = sqrt(5- (x^2 - 2)) = sqrt(5 -x^2 +2)

rArr h(g(x)) = sqrt(7 - x^2)