Question

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

Answer 1

`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)`