Question

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

Answer 1

Answer:

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

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

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

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

Step-by-step 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