Answer:
[tex]f(g(-1))=4[/tex]
[tex]g(f(3))=50[/tex]
Step-by-step explanation:
We know the definition of both functions: [tex]f(x)=3x-2[/tex], and [tex]g(x)=x^2+1[/tex]
A) In order to evaluate what [tex]f(g(-1)) is[/tex], let's first investigate what g(-1) is using the definition for this function:
[tex]g(x)=x^2+1\\g(-1)=(-1)^2+1\\g(-1)=1+1\\g(-1)=2[/tex]
Now let's find what f(2) is using f(x) definition: [tex]f(x)=3x-2\\f(2)=3(2)-2\\f(2)=6-2\\f(2)=4[/tex]
B) In order to evaluate what [tex]g(f(3)) is[/tex], let's first investigate what f(3) is using the definition for this function:
[tex]f(x)=3x-2\\f(3)=3(3)-2\\f(3)=9-2\\f(3)=7[/tex]
Now let's find what g(7) is using the definition for this function:
[tex]g(x)=x^2+1\\g(7)=(7)^2+1\\g(7)=49+1\\g(7)=50[/tex]
