Question

For questions 8 – 14, use the following functions:

f(x)=5

g(x)=sqrt x+2


8. Find (f+g(x).

9. Find (f-g)(x).

10. Find (f*g)(x).

11. Find (f/g)(x).
12. Find (g/f)(x).

13. Find (fog)(x)
14. Find (gof)(x)

Answer 1

we are given

`f(x)=5`

`g(x)=√(x+2)`

(8)

`(f+g)(x)=f(x)+g(x)`

we can plug it

`(f+g)(x)=5+√(x+2)`

(9)

`(f-g)(x)=f(x)-g(x)`

we can plug it

`(f-g)(x)=5-√(x+2)`

(10)

`(f*g)(x)=f(x)*g(x)`

we can plug it

`(f*g)(x)=5√(x+2)`

(11)

`((f)/(g) )(x)=(f(x))/(g(x))`

we can plug it

`((f)/(g) )(x)=(5)/(√(x+2))`

(12)

`((g)/(f) )(x)=(g(x))/(f(x))`

we can plug it

`((g)/(f) )(x)=(√(x+2))/(5)`

(13)

`(fog)(x)=f(g(x))`

`f(x)=5`

we can replace g(x)

we get

`(fog)(x)=5`

(14)

`(gof)(x)=g(f(x))`

`f(x)=5`

we can replace f(x)

`(gof)(x)=√(f(x)+2)`

we get

`(gof)(x)=√(5+2)`

`(gof)(x)=√(7)`