Answer:
[tex]15.~f(g(2))=\Large\boxed{11}\\[/tex]
[tex]16.~g(f(2.5))=\Large\boxed{16}[/tex]
[tex]17.~g(f(-5))=\Large\boxed{1}[/tex]
[tex]18.~f(g(-5))=\Large\boxed{-3}[/tex]
Step-by-step explanation:
Given information
[tex]f(x)=x+4[/tex]
[tex]g(x)=2x+3[/tex]
Question 15. f(g(2))
Substitute values into the first function
[tex]g(2)=2(2)+3[/tex]
[tex]g(2)=4+3[/tex]
[tex]g(2)=7[/tex]
Substitute the values of the first function into the second
[tex]f(g(2))=f(7)[/tex]
[tex]f(7)=(7)+4[/tex]
[tex]f(7)=\Large\boxed{11}[/tex]
Question 16. g(f(2.5))
Substitute values into the first function
[tex]f(2.5)=(2.5)+4[/tex]
[tex]f(2.5)=6.5[/tex]
Substitute the values of the first function into the second
[tex]g(f(2.5))=g(6.5)[/tex]
[tex]g(6.5)=2(6.5)+3[/tex]
[tex]g(6.5)=13+3[/tex]
[tex]g(6.5)=\Large\boxed{16}[/tex]
Question 17. g(f(-5))
Substitute values into the first function
[tex]f(-5)=(-5)+4[/tex]
[tex]f(-5)=-1[/tex]
Substitute the values of the first function into the second
[tex]g(f(-5))=g(-1)[/tex]
[tex]g(-1)=2(-1)+3[/tex]
[tex]g(-1)=-2+3[/tex]
[tex]g(-1)=\Large\boxed{1}[/tex]
Question 18. f(g(-5))
Substitute values into the first function
[tex]g(-5)=2(-5)+3[/tex]
[tex]g(-5)=-10+3[/tex]
[tex]g(-5)=-7[/tex]
Substitute the values of the first function into the second
[tex]f(g(-5))=f(-7)[/tex]
[tex]f(-7)=(-7)+4[/tex]
[tex]f(-7)=\Large\boxed{-3}[/tex]
Hope this helps!! :)
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