Question

Question #6be76

Answer 1

(i)`f@h(x)=sin(3x^2-1)`
(ii)`h@g(x)=3cos^2(x)-1`
(iii)`g@f(x)=cos(sinx)`
`gof(0)=1`

Explanation:

(i)`f@h(x)=f(h(x))=sin(h(x))=sin(3x^2-1)`

(ii)`h@g(x)=h(g(x))=3(g(x))^2-1=3cos^2(x)-1`

(iii)`g@f(x)=g(f(x))=cos(f(x))=cos(sinx)`

(iv)`g@f(0)=g(f(0))`
Using the computed composition in (iii):

`gof(0)=cos(sin0)=cos(0)=1`