Question

F(x) = x + 4 and g(x) = 2x + 3, evaluate each expression.

15. f(g(2))

16.g(f(2.5))

17. g(f(-5))

18. f(g(-5))

Answer 1

`15.~f(g(2))=\Large\boxed{11}\\`

`16.~g(f(2.5))=\Large\boxed{16}`

`17.~g(f(-5))=\Large\boxed{1}`

`18.~f(g(-5))=\Large\boxed{-3}`

Explanation:

Given information

`f(x)=x+4`

`g(x)=2x+3`

Question 15. f(g(2))

Substitute values into the first function

`g(2)=2(2)+3`

`g(2)=4+3`

`g(2)=7`

Substitute the values of the first function into the second

`f(g(2))=f(7)`

`f(7)=(7)+4`

`f(7)=\Large\boxed{11}`

Question 16. g(f(2.5))

Substitute values into the first function

`f(2.5)=(2.5)+4`

`f(2.5)=6.5`

Substitute the values of the first function into the second

`g(f(2.5))=g(6.5)`

`g(6.5)=2(6.5)+3`

`g(6.5)=13+3`

`g(6.5)=\Large\boxed{16}`

Question 17. g(f(-5))

Substitute values into the first function

`f(-5)=(-5)+4`

`f(-5)=-1`

Substitute the values of the first function into the second

`g(f(-5))=g(-1)`

`g(-1)=2(-1)+3`

`g(-1)=-2+3`

`g(-1)=\Large\boxed{1}`

Question 18. f(g(-5))

Substitute values into the first function

`g(-5)=2(-5)+3`

`g(-5)=-10+3`

`g(-5)=-7`

Substitute the values of the first function into the second

`f(g(-5))=f(-7)`

`f(-7)=(-7)+4`

`f(-7)=\Large\boxed{-3}`

Hope this helps!! :)

Please let me know if you have any questions