Answer:
[tex]g(f(x))( - 1) = 6[/tex]
Step-by-step explanation:
This is what you Composite Function, in this case it says g[f(x)] or g compose f so we need to find that equation.
[tex]f(x) = 3x + 1 \\ g(x) = {x}^{2} + 2[/tex]
Substitute the value of f(x) to g(x)
[tex]g(x) = {x}^{2} + 2 \\ g(f(x)) = {(3x + 1)}^{2} + 2 \\ g(f(x)) = 9 {x}^{2} + 6x + 1 + 2 \\ g(f(x)) = 9 {x}^{2} + 6x + 3[/tex]
Now we need to find the value of the function when x = -1
[tex]g(f(x))(x) = 9 {x}^{2} + 6x + 3 \\ g(f(x))( - 1) = 9 {( - 1)}^{2} + 6( - 1) + 3 \\ g(f(x))( - 1) = 9 - 6 + 3 \\ g(f(x))( - 1) = 6[/tex]
So thw answer is 6
